A certain type of component is packaged in lots of four. Let X represents the number of properly functioning components in a randomly chosen lot. Assume that the probability that exactly x components function is proportional to x; in other words, assume that the probability mass function of X is given by

Where c is a constant.
a. Find the value of the constant c so that p(x) is a probability mass function.
b. Find P(X = 2).
c. Find the mean number of properly functioning components.
d. Find the variance of the number of properly functioning components.
e. Find the standard deviation of the number of properly functioning components.

Transcribed Image Text:

p(x)-,cr x=1, 2, 3, or4 otherwise I. 2, 3, or