e that the random variable X denotes temperature on the Celsius scale and that t

Question

e that the random variable X denotes temperature on the Celsius scale and that the random variable Y denotes temperatures on the Fahrenheit scale. We know that Y = (9/5X + 32.0 a) [5] If daily temperatures during September follow a distribution with a mean of 15 degrees Celsius and a standard deviation of 5 degrees Celsius, what is the mean and the standard deviation of the temperature on the Fahrenheit scale? b) [5] By working out and showing the relevant components of the calculation, compute the correlation coefficient between X and Y

Explanation / Answer

Ans:

E[X]=15

Var(X)=52=25

a)E[Y]=(9/5)E[X]+32=1.8*15+32=59

Var(Y)=(9/5)2*Var(X)=81

std. dev of Y=9

b)

slope,b=r*sy/sx

r=b*sx/sy=(9/5)*(5/9)=1

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