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Recent questions tagged random-variable

1 vote
1 answer
1
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n-1}$ $\frac{1}{n-2}$
asked Sep 23, 2019 in Probability Arjun 387 views
1 vote
1 answer
2
If a student copies his assignments from his friend he would get 80 marks. If he had done the assignments independently he would have scored 50 marks out of 100 and if the teacher finds he is cheating he will be penalized and will be given 0 marks. ... he copies 10 such assignments, what is the probability that he will lose more marks with copying than by doing his independent work independently?
asked May 28, 2019 in Probability Asim Siddiqui 4 359 views
0 votes
1 answer
3
A carnival swing ride swings to the left with probability 0.4 and to the right with probability. If the ride stops after 10 swings, what is the probability that it is exactly at the place it started?
asked May 27, 2019 in Probability Asim Siddiqui 4 243 views
1 vote
2 answers
4
An airline operates a flight having 50 seats. As they expect some passenger to not show up, they overbook the flight by selling 51 tickets. The probability that an individual passenger will not show up is 0.01, independent of all other tourists. Each ticket costs Rs ... not available, the airline has to pay a compensation of Rs.1lakh to that passenger. What is the expected revenue of the airline?
asked May 21, 2019 in Probability Asim Siddiqui 4 237 views
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6
Suppose that the cdf of X is given by: F(a) ={ 0 for a < 0 1/5 for 0 ≤ a < 2 2/5 for 2 ≤ a < 4 1 for a ≥ 4. } Determine the pmf of X.
asked Feb 19, 2019 in Probability Na462 184 views
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8
Suppose that the running time for each process in milliseconds is an exponential random variable with parameter λ=1/20. If process P1 arrives immediately ahead of the process P2 in the running state, then the probability that process P2 will have to wait more than 20 milliseconds is _____________ . A 0.274 B 0.324 C 0.428 D 0.368 How to approach this. even not able to understand the question.
asked Jan 27, 2019 in Operating System Ashish Goyal 103 views
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9
Probability density function of a random variable X is distributed uniformly between 0 and 10 The probability that X lies between 2.5 to 7.5 and the mean square value of X are respectively. please give step by step answer in a detailed manner.
asked Jan 21, 2019 in Probability learner_geek 180 views
1 vote
3 answers
10
In a lottery, 10 tickets are drawn at random out of 50 tickets numbered from 1 to 50. What is the expected value of the sum of numbers on the drawn tickets?
asked Jan 20, 2019 in Mathematical Logic learner_geek 982 views
1 vote
1 answer
11
A player tosses two fair coins. He wins rs 2 if 2 heads occur and rs 1 if 1 head occurs. On the other hand, he loses rs 3 if no heads occur. if the player plays 100 times.then the amount he wins______________(RS).
asked Jan 20, 2019 in Mathematical Logic learner_geek 232 views
0 votes
0 answers
12
This is an example in the book (A First Course in Probability by Sheldon Ross). A stick of length 1 is split at a point U that is uniformly distributed over (0,1). Determine the expected length of the piece that contains the point 0≤p≤1. So, My doubt here(see the blue mark) is according to proposition g(x) is Lp(U) , what is f(x) why f(x) is not multiplied. in calculating expected value.
asked Jan 9, 2019 in Probability Sandy Sharma 240 views
1 vote
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13
A continuous random variable $x$ is distributed over the interval $[0,2]$ with probability density function $f(x) =ax^2 +bx$, where $a$ and $b$ are constants. If the mean of the distribution is $\frac{1}{2}$. Find the values of the constants $a$ and $b$. $a=2, b=- \frac{13}{6}$ $a= – \frac{15}{8}, b=3$ $a= – \frac{29}{6}, b=2$ $a=3, b= – \frac{7}{2}$
asked Dec 7, 2018 in Probability Arjun 506 views
1 vote
0 answers
15
Find the value of $\lambda$ such that function f(x) is valid probability density function $f(x)=\lambda (x-1)(2-x)$ for $1 \leq x \leq 2$ $=0$ otherwise My $\lambda$ is coming to be $- \frac{6}{5}$ Am I correct?
asked Nov 15, 2018 in Probability Ayush Upadhyaya 392 views
1 vote
1 answer
16
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, 2018 in Probability Gaurangi Katiyar 199 views
0 votes
0 answers
17
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, 2018 in Probability Pooja Khatri 129 views
0 votes
1 answer
18
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, 2018 in Probability Pooja Khatri 126 views
0 votes
1 answer
19
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, 2018 in Probability Pooja Khatri 136 views
1 vote
0 answers
20
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, 2018 in Probability Pooja Khatri 78 views
0 votes
0 answers
21
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, 2018 in Probability Pooja Khatri 80 views
1 vote
1 answer
22
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) Assume that you know in advance ... . Let $M$ be the amount of time of the show that you miss because of th call. Compute the expected value of $M$.
asked Sep 27, 2018 in Probability Pooja Khatri 147 views
0 votes
1 answer
23
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, 2018 in Probability Pooja Khatri 112 views
0 votes
1 answer
24
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, 2018 in Probability Pooja Khatri 118 views
0 votes
1 answer
25
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, 2018 in Probability Pooja Khatri 120 views
0 votes
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26
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, 2018 in Probability Pooja Khatri 75 views
0 votes
1 answer
27
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, 2018 in Probability Pooja Khatri 90 views
0 votes
1 answer
28
How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
asked Sep 26, 2018 in Probability Pooja Khatri 84 views
0 votes
0 answers
29
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, 2018 in Probability Pooja Khatri 67 views
0 votes
2 answers
30
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, 2018 in Probability Pooja Khatri 379 views
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