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Recent questions tagged randomvariable
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Continous Probability
Find the value of $\lambda$ such that function f(x) is valid probability density function $f(x)=\lambda (x1)(2x)$ for $1 \leq x \leq 2$ $=0$ otherwise My $\lambda$ is coming to be $ \frac{6}{5}$ Am I correct?
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Probability
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Ayush Upadhyaya
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Made easy workbook
Suppose the random variable X has the probability distribution given below: X 2 1 0 1 2 P(X=X) 0.25 0.20 0.15 0.35 0.05 Let $Y=(2*(X^2))+6$.The expected value E(Y) is: A) 9.5 B) 6. C )15.5. D )18
asked
Nov 8
in
Probability
by
Gaurangi Katiyar
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35
points)

52
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randomvariable
probability
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3
Probability Gravner 82.c
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (c) How large should $n$ be so that the probability in(b) is larger than $0.99$?
asked
Sep 27
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Probability
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Pooja Khatri
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5k
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37
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Probability Gravner 82.b
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (b) Write down an approximation, in terms on $n$ and $\phi$, of the probability that $M$ differs from its expectation by less than $10$ %
asked
Sep 27
in
Probability
by
Pooja Khatri
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5k
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33
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probability
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Probability Gravner 82.a
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (a) Compute the expectation $EM$.
asked
Sep 27
in
Probability
by
Pooja Khatri
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5k
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35
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gravner
probability
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Probability Gravner 81.b
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (b) Approximately how many times do you need to play so that you win at least $250$ dollar with probability at least $0.99$.
asked
Sep 27
in
Probability
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Pooja Khatri
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5k
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23
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probability
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Probability Gravner 81.a
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (a) Assume that you play this game $300$ times. What is, approximately, the probability that you win at least $250$ dollar ?
asked
Sep 27
in
Probability
by
Pooja Khatri
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5k
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20
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probability
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Probability Gravner 80.c
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (c) ... $M$ be the amount of time of the show that you miss because of th call. Compute the expected value of $M$.
asked
Sep 27
in
Probability
by
Pooja Khatri
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5k
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18
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probability
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uniformdistribution
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Probability Gravner 80.b
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval (b) At $8.30$, the call still hasn't arrived. What is the probability that it arrives in the next $10$ minutes?
asked
Sep 27
in
Probability
by
Pooja Khatri
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5k
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15
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probability
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uniformdistribution
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votes
1
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Probability Gravner 80
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (a) Compute the probability that the call arrives between $8.30$ and $8.20$.
asked
Sep 27
in
Probability
by
Pooja Khatri
Active
(
5k
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14
views
probability
gravner
engineeringmathematics
randomvariable
uniformdistribution
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Probability Gravner 79.c
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (c) Determine the probability density function of $Y$ $=$ $X^2$
asked
Sep 26
in
Probability
by
Pooja Khatri
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5k
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13
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probability
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randomvariable
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Probability Gravner 79.b
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (b) Compute $\text{E(1/X)}$.
asked
Sep 26
in
Probability
by
Pooja Khatri
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5k
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11
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probability
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randomvariable
0
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1
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13
Probability Gravner 79.a
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (a) Determine c.
asked
Sep 26
in
Probability
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Pooja Khatri
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5k
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23
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gravner
probability
engineeringmathematics
randomvariable
0
votes
1
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Probability Gravner 78
How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
asked
Sep 26
in
Probability
by
Pooja Khatri
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5k
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16
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probability
gravner
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randomvariable
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Probability Gravner 77
A roulette wheel has $38$ slots: $18$ red, $18$ red, $2$ green. The ball ends at one of these at random. You are a player who plays a large number of games and makes an even bet of $1$ dollar on red in every game. After $n$ games, what is the probability that you are ahead? Answer this for $n=100$ and $n= 1000$.
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
5k
points)

9
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
2
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16
Probability Gravner 76
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
asked
Sep 26
in
Probability
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Pooja Khatri
Active
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5k
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42
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probability
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randomvariable
normaldistribution
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votes
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17
Probability Gravner 75.c
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
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5k
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16
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probability
gravner
engineeringmathematics
randomvariable
0
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1
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18
Probability Gravner 75.b
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
5k
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15
views
probability
gravner
engineeringmathematics
randomvariable
0
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19
Probability Gravner 75.a
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
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5k
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16
views
gravner
probability
engineeringmathematics
randomvariable
normaldistribution
+1
vote
1
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20
Probability  Gravner74
Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ > $0$. How is $Y$ distributed?
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
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5k
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36
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probability
gravner
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randomvariable
normaldistribution
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votes
1
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21
Probability  Gravner73
Assume that a light bulb lasts on average $100$ hours. Assuming exponential distribution, compute the probability that it lasts more than $200$ hours and the probability that it lasts less than $50$ hours.
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
5k
points)

27
views
probability
gravner
engineeringmathematics
randomvariable
0
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0
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22
Probability  Gravner72
A uniform random number $X$ divides $[0,1]$ into two segments. Let $R$ be the ratio of the smaller versus the larger segment. Compute the density of $R$.
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
5k
points)

7
views
probability
gravner
engineeringmathematics
randomvariable
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votes
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23
Probability  Gravner71
Assume that X is uniform on [0,1]. What is $P(X\epsilon Q)$? What is the probability that the binary expansion of X starts with 0.010?
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
5k
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11
views
probability
gravner
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randomvariable
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24
Probability  Gravner70
Assume that X has density $fx(x) = \begin{Bmatrix} 3x^{2} &if(x\epsilon [0,1]), \\ 0& otherwise \end{Bmatrix}$ Compute the density fy of Y= 1X4
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
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5k
points)

6
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probability
gravner
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25
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
asked
Sep 26
in
Probability
by
Pooja Khatri
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5k
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6
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probability
gravner
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26
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (b) Compute $P(1\leqslant X\leqslant 2)$
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
5k
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7
views
probability
gravner
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randomvariable
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0
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27
Probability  Gravner69.a
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
asked
Sep 26
in
Probability
by
Pooja Khatri
Active
(
5k
points)

6
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gravner
probability
engineeringmathematics
randomvariable
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Probability  Gravner68.d
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student's ... of the randomly chosen group. Let EY= $\mu$ and Var(Y) = $\sigma$2 . Express EX with s, n, $\mu$ and $\sigma$.
asked
Sep 25
in
Probability
by
Pooja Khatri
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5k
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13
views
gravner
probability
engineeringmathematics
randomvariable
0
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29
Probability  Gravner68.c
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student's group . Next, choose one the four groups at random and let $Y$ be its size. (c) Compute Var(X) and Var(Y).
asked
Sep 25
in
Probability
by
Pooja Khatri
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5k
points)

8
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gravner
probability
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randomvariable
0
votes
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Probability  Gravner68.b
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student's group . Next, choose one the four groups at random and let $Y$ be its size. (b) Compute EX and EY.
asked
Sep 25
in
Probability
by
Pooja Khatri
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5k
points)

7
views
gravner
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