Grinstead-Snell-Probability · Problem 5

Expected Value and Variance

Mathematics · variance-discrete-random-variables

Problem

In a certain manufacturing process, the (Fahrenheit) temperature never varies by more than

2^\circ

from

62^\circ

. The temperature is, in fact, a random variable

F

with distribution

P_F = \begin{pmatrix} 60 & 61 & 62 & 63 & 64 \\ 1/10 & 2/10 & 4/10 & 2/10 & 1/10 \end{pmatrix}.

((a)) Find

E(F)

and

V(F)

. ((b)) Define

T = F - 62

. Find

E(T)

and

V(T)

, and compare these answers with those in part (a). ((c)) It is decided to report the temperature readings on a Celsius scale, that is,

C = (5/9)(F - 32)

. What is the expected value and variance for the readings now?