1. The following probability distribution represents the numberof people living in a Household (X), and the probability ofoccurrence (P(X)). Compute the Expected Value (mean), the Varianceand the Standard Deviation for this random variable. Show YourCalculations for the Mean.
   X     1        2       3        4       5              Â
P(X)Â Â Â .33 Â Â Â Â .29Â Â Â Â .27 Â Â Â Â Â Â .07 Â Â Â Â Â .04 Â Â Â Â
2. Use the binomial formula to compute the probability of astudent getting 8 correct answers on a 10 question Quiz, if theprobability of answering any one question correctly is 0.64.SHOW YOUR WORK.
3. Submit your answers to the following binomial questions. Youmay use the appendix table B #5 to answer parts (a) and (b).According to a government study, 20% of all children live in ahousehold that has an income below the poverty level. If a randomsample of 15 children is selected:
a) what is the probability that 6 or more live in poverty?
b) what is the probability that 5 live in poverty?
c) what is the expected number (mean) that live in poverty?
