Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.9. Assume that the trials are independent.

a.) Calculate the variance of x.

b.) Calculate the variance of x.

c.) Determine the probability mass function of the number of trials (x) required until the first successful alignment.

d.) Find the probability that the first successful alignment requires trials four trials at the maximum.

SEND ALL ANSWERS IN HANDWRITTEN SOLUTIONS. THREE DECIMAL PLACES. THANK YOU!