MHT-CET Probability Distributions — practice questions
45 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice MHT-CET Probability Distributions in the app →A random variable is a real-valued function defined on what?The number of heads in 4 coin tosses is which kind of variable?How are the values of a discrete random variable obtained?A continuous random variable takes how many possible values?Which of these is a continuous random variable?The probabilities in a probability distribution add up to what?Each probability pi in a p.m.f. must be at least what?A head has probability t. What is P(first head on the 3rd toss)?For a discrete random variable X, the c.d.f. F(x) equals?What is E(X) for the number of heads in two fair coin tosses?A fair die is thrown once. What is the expected score?X takes 1, 2, 3 with probabilities 0.2, 0.5, 0.3. Find E(X).A game scores 1, 2 or 3 with chances 20%, 50% and 30%. What is the variance of the score?Outcomes 0, 1, 2 occur with chances 1/4, 1/2, 1/4. Compute the variance.Four values 1 to 4 have chances 0.1, k, 0.3 and 0.4 respectively. What is k?P(X = x) = kx for x = 1, 2, 3, 4 is a p.m.f. Find k.The standard deviation of a random variable is defined as?X is the score on a fair die. Find Var(X).A die game pays Rs 18 for an even score and costs Rs 6 for an odd one. Expected gain?X is the number of sixes in two die rolls. Find P(X = 0).The distribution of a continuous variable is described using a?For a continuous random variable X, P(X = c) for a single point c is?A p.d.f. f(x) must satisfy which condition on its support S?The total area under a p.d.f. curve over its support is?f(x) = 3x^2 on 0 < x < 1. Find P(X < 1/2).For a continuous variable, probabilities are given by?X is uniform on 0 to 4 with f(x) = 1/4. Find P(1 < X < 3).In F(x) for a continuous X on (a, b), the integral of f(t) runs from?How many outcomes does each Bernoulli trial have?Bernoulli trials must be which of the following?A die is thrown 50 times with an even score as success. This is?For X ~ B(n, p), what is P(X = x)?In B(n, p), how many different values can X take?Why do the binomial probabilities add up to 1?If X ~ B(10, 0.4), what is E(X)?The mean of a binomial distribution B(n, p) is?If X ~ B(4, 1/3), find P(X = 2).X ~ B(4, p) and P(X = 0) = 16/81. Find p.X ~ B(6, p) with P(X = 2) = P(X = 4). Find p.A die is rolled 4 times. Expected number of sixes?A coin is tossed 100 times. Variance of the number of heads?The number of successes in 3 Bernoulli trials can be?For 3 Bernoulli trials, P(exactly one success) is?P(X = 1, 2, 3) = 0.2, 0.5, 0.3. Find F(2).Two fair dice are rolled. What is P(sum is 2)?