Question

x= 0,1,2,3

P(X)= .1, .3, .4, .2

(a) Verify that the two requirements for a discrete probability distribution are satisfied. (b) Find the mean (expected value), variance, and standard deviation of this distribution. (c) What is the probability that there is less than two pizza deliveries to a university student in a month? (d) What is the probability that there is at least two pizza deliveries to a university student in a month?

Answer 1

(a) Note that (i) P(x) >0

(ii) sum of probabilities = 0.1+0.3+0.4+0.2 = 1

(b) Mean=E(X) = sum(xP(x)) = (0*0.1)+(1*0.3)+(2*0.4)+(3*0.2) = 1.7

E(X²) = sum(x²P(x)) = (0*0.1)+(1*0.3)+(4*0.4)+(9*0.2) = 3.7

Var(X) = E(X²)-E(X)² = 3.7-(1.7*1.7) = 0.81

SD(X) = sqrt(Var) = sqrt(0.81) = 0.9

(c) P(X<2) = P(0)+P(1) = 0.1+0.3 = 0.4

P(X>=2) = P(2) +P(3) = 0.4+0.2 = 0.6