Question: The reading given by a thermometer calibrated in ice water (actual temperature 0C) is a random variable with probability density function f(x) = {k(1

The reading given by a thermometer calibrated in ice water (actual temperature 0◦C) is a random variable with probability density function f(x) =

{k(1 − x2) −1 < x < 1 0 otherwise where k is a constant.

a. Find the value of k.

b. What is the probability that the thermometer reads above 0◦C?

c. What is the probability that the reading is within 0.25◦C of the actual temperature?

d. What is the mean reading?

e. What is the standard deviation of the readings?

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