search
Log In

Recent questions tagged random-variable

4 votes
1 answer
1
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
asked Feb 18 in Probability Arjun 732 views
2 votes
2 answers
2
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
asked Feb 18 in Probability Arjun 895 views
1 vote
1 answer
3
Consider the two statements. $S_1:\quad$ There exist random variables $X$ and $Y$ such that $ \left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2>\textsf{Var}[X]\textsf{Var}[Y]$ $S_2:\quad$ For all random variables $X$ ... Both $S_1$ and $S_2$ are true $S_1$ is true, but $S_2$ is false $S_1$ is false, but $S_2$ is true Both $S_1$ and $S_2$ are false
asked Feb 18 in Probability Arjun 654 views
0 votes
0 answers
4
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ where $\Phi(a=-2)=0.02,$ ... less than 0.02 $\int^{18} _{-\infty} \frac{1}{\sqrt{2\pi .2^2}}\exp\{-\frac{1}{2}(\frac{x-24}{2})^2\}dx$
asked Jan 29 in Others soujanyareddy13 84 views
0 votes
0 answers
5
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ where $\Phi(a=-2)=0.02,$ ... more than 0.4 less than 0.5
asked Jan 29 in Others soujanyareddy13 42 views
0 votes
0 answers
6
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ ... will last more than $26$ months approximately equals $16\%$ is more than $15\%$ is less than $14\%$ is between $10\%$ and $15\%$
asked Jan 29 in Others soujanyareddy13 39 views
1 vote
1 answer
7
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 477 views
1 vote
1 answer
8
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 4 436 views
0 votes
1 answer
9
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 4 314 views
1 vote
2 answers
10
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 4 302 views
0 votes
0 answers
11
0 votes
0 answers
12
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 236 views
0 votes
1 answer
14
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 155 views
0 votes
0 answers
15
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 235 views
2 votes
3 answers
16
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 1.2k views
1 vote
1 answer
17
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 294 views
0 votes
0 answers
18
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 746 views
1 vote
0 answers
19
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 942 views
1 vote
0 answers
21
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 656 views
1 vote
1 answer
22
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 271 views
0 votes
0 answers
23
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 191 views
1 vote
1 answer
24
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 233 views
0 votes
1 answer
25
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 205 views
1 vote
0 answers
26
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 93 views
0 votes
0 answers
27
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 99 views
1 vote
1 answer
28
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 205 views
0 votes
1 answer
29
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 151 views
0 votes
1 answer
30
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 216 views
...