Probability Distributions: JEE Questions & Solutions

A random variable X takes values 0, 1, 2, 3 with probabilities (2a+1)/30, (8a-1)/30, (4a+1)/30, b respectively, where a, b ∈ ℝ. Let μ and σ…

If a random variable x has the probability distribution | x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---|---| | P(x)…

From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of…

The probability distribution of a random variable X is given below: x 4k 30k/7 32k/7 34k/7 36k/7 38k/7 40k/7 6k P(X) 2/15 1/15 2/15 1/5…

A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ² denote the mean and variance of X, then…

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between…

Let A = [a_ij] be a 2 × 2 matrix such that a_ij ∈ {0, 1} for all i and j. Let the random variable X denote the possible values of the…

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the…

If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)3^(-x), x = 0, 1, 2, 3, …, where k is a…

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then…

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(X²) = 2E(X). Then the value of 8p -…

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a…

Three rotten apples are accidentally mixed with seven good apples, and four apples are drawn one by one without replacement. Let the random…

In a binomial distribution B(n, p), the sum and product of the mean and variance are 5 and 6, respectively. Then 6(n + p - q) is equal to:

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is…

Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine…

Let the probability of getting a head for a biased coin be 1/4. It is tossed repeatedly until a head appears. Let N be the number of tosses…

Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is p/q, where p and q…

A fair n > 1 faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is n/9, then n…

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or 3 tails occur. If X denotes…

The random variable X follows binomial distribution B(n, p), for which the difference of the mean and the variance is 1. If 2P(X = 2) =…