Answer:
a. This is a probability distribution as ∑pi=1
b. 2.72
c. 1.45
Step-by-step explanation:
a. To verify the probability distribution we simply add all given probabilities and see whether they sums up to 1 or not. According to definition of probability distribution sum of probabilities should be 1 so,
∑pi=0.32+0.12+0.23+0.18+0.15=1
Hence it is verified that given distribution is a probability distribution.
b. Mean number of items selected= E(x)= ∑x*p(x)
here x =1,2,3,4,5 and p(x)=0.32,0.12,0.23,0.18,0.15.
mean number of items=1*0.32+2*0.12+3*0.23+4*0.18+5*0.15=2.72
c. standard deviation of number of items=sqrt[(∑x²*p(x))-(∑x*p(x))²]
∑x²*p(x)=1*0.32+4*0.12+9*0.23+16*0.18+25*0.15=9.5
(∑x*p(x))²=(2.72)²=7.4
standard deviation of number of items=sqrt[(∑x²*p(x))-(∑x*p(x))²]=sqrt(9.5-7.4)=sqrt(2.1)=1.45
