1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable.X 1 2 3 4 5 6 7P(X) .22 .35 .18 .13 .07 .03 .022. Use the binomial formula to compute the probability of a student getting 3 correct answers on a 7 question Quiz, if the probability of answering any one question correctly is 0.83. SHOW YOUR WORK.3. Submit your answers to the following binomial questions. You may use the appendix tables 5 to answer parts a and b. According to a government study,15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:a) what is the probability that 4 or more live in poverty?b) what is the probability that 3 live in poverty?c) what is the expected number (mean) that live in poverty?