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Recent questions tagged random-variable

8 8 votes
2 2 answers
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TIFR CSE 2014 | Part A | Question: 19
Consider the following random function of $x$$F(x) = 1 + Ux + Vx^{2} \bmod 5$,where $U$ and $V$ are independent random variables uniformly distributed over $\left\{0, 1, ...
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6 6 votes
1 answers 1 answer
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TIFR CSE 2013 | Part A | Question: 18
Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (betwee...
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13 13 votes
2 answers 2 answers
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random variables
Consider two independent random variables $X$ and $Y$ with identical distributions.The variables $X$ and $Y$ take value $0, 1$ and $2$ with probabilities $\frac{1}{2},\fr...
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3 3 votes
1 1 answer
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Probability
Suppose that the length of the phone calls in minutes is an exponential random variable with parameter $\lambda = 1/10$.If someone arrives immediately ahead of you at a p...
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15 15 votes
1 answers 1 answer
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TIFR CSE 2011 | Part A | Question: 7
Let $X$ and $Y$ be two independent and identically distributed random variables. Then $P\left ( X Y \right )$ is.$\frac{1}{2}$10$\frac{1}{3}$Information is insufficient.
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3 3 votes
1 answers 1 answer
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Continuous random distribution
The continuous random variable X has pdf f(x)=x/2, 0<=x<=2. Two independent determinations of X are made. What is the probability that both these determinations will be g...
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1 1 vote
2 2 answers
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Random variables and distribution
If X is a continuous random variable whose probability density function is given byf(x) ={k(5x-2x^2) , 0
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3 3 votes
4 4 answers
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Uniform probability distribution
X is uniformly distributed random variable that takes values between 0 and 1.The value of E(X^3) will be
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73 73 votes
10 answers 10 answers
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GATE CSE 2015 | Set 3 | Question: 37
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} ...
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1 1 vote
0 0 answers
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Let X be the random variable on the set of permutations of a set of n distinct integers {a 1 , a 2 , . . . , a n } with a1 < a2 < · · · < an such that X(P) equals the number of comparisons used by the bubble sort to put these integers into increasing order.
Answer the following part:a) Show that, under the assumption that the input is equally likely to be any of the n! permutations of theseintegers, the average number of com...
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2 2 votes
2 answers 2 answers
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You are asked to open one door. There is a large prize behind one of the three doors and the other two doors are losers.
You are asked to open one door. There is a large prize behind one of the three doors and the other two doors are losers. After you select a door, Monty Hall opens one of ...
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73 73 votes
4 answers 4 answers
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GATE IT 2004 | Question: 33
Let $X$ and $Y$ be two exponentially distributed and independent random variables with mean $α$ and $β$, respectively. If $Z$ = min $(X, Y)$, then the mean of $Z$ is give...
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46 46 votes
6 answers 6 answers
15.2k
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GATE CSE 2011 | Question: 33
Consider a finite sequence of random values $X=[x_1,x_2,\dots x_n]$. Let $\mu_x$ be the mean and $\sigma_x$ be the standard deviation of $X$. Let another finite sequence ...
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54 54 votes
7 answers 7 answers
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GATE CSE 2011 | Question: 18
If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\l...
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61 61 votes
6 answers 6 answers
21.1k
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GATE CSE 2012 | Question: 21
Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and $+1$...
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32 32 votes
3 answers 3 answers
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GATE CSE 2005 | Question: 12, ISRO2009-64
Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is :$f(b-a)$$f(b) - f(a)$$\int\limits_a^b f(x) dx...
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61 61 votes
5 answers 5 answers
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GATE CSE 2003 | Question: 60, ISRO2007-45
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ respectively denote the probability density functions of time taken to execute the two ...
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71 71 votes
5 answers 5 answers
32.5k
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GATE CSE 2008 | Question: 29
Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P ...
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7 7 votes
2 answers 2 answers
2.6k
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random variable $X^2+Y^2 >1$
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1, 1]$. The probability that $X^{2}+Y^{2}>1$ is $\pi...
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