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# ESE Achiever's plan || Paper 1 || Probability & Distribution

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Question 1

A single die is rolled six times, the probability that the six outcomes are all different is

Question 2

Let X ϵ {0, 1} be two independent binary random variables. If P(X = 0) = P and P(Y = 0) = q, then P(X + Y ≥ 1) is equal to

Question 3

The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is _________.

Question 4

Two random variables X and Y are distributed according to

The probability is

The probability is

Question 5

A and B throw alternatively a pair of dice . A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6 . If ‘A’ starts the game, then the probability that B wins the game is

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Jun 5ESE & GATE EC

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