Probability & Statistics

What is P(AUBUC) formula? Question : Suppose are events in a common probability space with P(A) =0.2 , P(B) =0.2, P(C) =0.3, P(A∩B) =0.1 , P(A∩C) =0.1, P(B∩C) = 0.1…

Question : From the six letters P, Q, R, S, T and U, three letters are chosen at random with replacement. What is the probability that either the word “QPS”…

Question : What is Bernoulli Distribution ? Answer : Bernoulli Distribution : If a random variable X has only two possibilities to occur then it is called Bernoulli random variable.…

Question : Prove that the variance of cX+d is c^2 V(X)+d where X is a continuous random variable. Solution : We know that variance of a continuous random variable is…

Question : Prove that the mean of cX+d = E(X)+d where X is a continuous random variable. Solution : We know that Expectation of a continuous random variable is \[E\left(X\right)=\int_{-\infty}^{\infty}xf\left(x\right)dx\]…

Question : how to find expectation of a function of random variable ? x0123f(x)1/83/83/81/8 Find (i) E[X]        (ii) E[X^2]            (iii) E[3X-2]      (iv)  E[(X+1)^2] Solution : Fo the given probability distribution…

Question : Find expectation of the following probability distribution x0123f(x)1/83/83/81/8 Solution : Given probability distribution of a random variable X is x0123f(x)1/83/83/81/8 Since values of x are 0,1,2,3 are finite.…

Question : what are following probabilities if we toss three fair coins ? (i) Probability of getting two tails. (ii) Probability of getting two heads. (iii) Probability of getting two…

Question : Find the probability of getting two and one tail if we the toss three fair coins. Solution : Let H denotes head and T denotes tail. If we…

Question : Find the probability mass function of the heads in the tossing of three fair coins. Solution : Sample space of tossing of three fair coins is given as…