JEE MAIN Probability Distribution Previous Year Questions (PYQs) – Page 1 of 3
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Let X be a random variable such that the probability function of a distribution is given by $P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$. Then the mean of the distribution and P(X is positive and even) respectively are :
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If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and ${{37} \over 4}$ respectively, then (a $-$ b)2 is equal to :
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The mean of the following probability distribution of a random variable $X$ is $\dfrac{46}{9}$.
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A person throws two fair dice. He wins Rs. $15$ for throwing a doublet (same numbers on the two dice), wins Rs. $12$ when the throw results in the sum of $9$, and loses Rs. $6$ for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:
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A six faced die is biased such that
$3 \times P(\text{a prime number}) = 6 \times P(\text{a composite number}) = 2 \times P(1).$
Let $X$ be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of $X$ is:
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Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is $k{\left( {{3 \over 4}} \right)^9}$ then k lies in the set :
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A random variable X has the following probability distribution :
The value of P(1 < X < 4 | X $\le$ 2) is equal to :
The value of P(1 < X < 4 | X $\le$ 2) is equal to :
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Let a random variable $X$ take values $0,1,2,3$ with $P(X=0)=P(X=1)=p$, $P(X=2)=P(X=3)$ and $E(X^2)=2E(X)$. Then the value of $8p-1$ is:
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The probability that the random variable $X$ takes value $x$ is given by
$P(X = x) = k(x + 1)3^{-x}, \; x = 0, 1, 2, 3, \ldots$
where $k$ is a constant. Then $P(X \ge 2)$ is equal to:
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Three defective oranges are accidentally mixed with seven good ones and, on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denotes the number of defective oranges, then the variance of $x$ is
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