Answer:
1. E(Y) = 50.54°F
2. SD(Y) = 11.34°F
Step-by-step explanation:
We are given that The daily high temperature X in degrees Celsius in Montreal during April has expected value E(X) = 10.3°C with a standard deviation SD(X) = 3.5°C.
The conversion of X into degrees Fahrenheit Y is Y = (9/5)X + 32.
(1) Y = (9/5)X + 32
E(Y) = E((9/5)X + 32) = E((9/5)X) + E(32)
= (9/5) * E(X) + 32 { expectation of constant is constant}
= (9/5) * 10.3 + 32 = 50.54
Therefore, E(Y), the expected daily high in Montreal during April in degrees Fahrenheit is 50.54°F .
(2) Y = (9/5)X + 32
SD(Y) = SD((9/5)X + 32) = SD((9/5)X) + SD(32)
= * SD(X) + 0 {
standard deviation of constant is zero}
=
* 3.5 = 11.34°F
Therefore, SD(Y), the standard deviation of the daily high temperature in Montreal during April in degrees Fahrenheit is 11.34°F .