In a certain manufacturing process, the (Fahrenheit) temperature never varies by more than [math]2^\circ[/math] from [math]62^\circ[/math]. The temperature is, in fact, a random variable [math]F[/math] with distribution

[[math]] P_F = \pmatrix{ 60 & 61 & 62 & 63 & 64 \cr 1/10 & 2/10 & 4/10 & 2/10 & 1/10 \cr}\ . [[/math]]

• Find [math]E(F)[/math] and [math]V(F)[/math].
• Define [math]T = F - 62[/math]. Find [math]E(T)[/math] and [math]V(T)[/math], and compare these answers with those in part (a).
• It is decided to report the temperature readings on a Celsius scale, that is, [math]C = (5/9)(F - 32)[/math]. What is the expected value and variance for the readings now?