The following depicts a probability density function (PDF) for the random variab

Question

The following depicts a probability density function (PDF) for the random variable X representing temperature. (a) Is this a continuous or discrete random variable? (b) Calculate what p must be in order for this to be a true PDF. (c) Calculate the probability that the random variable lies between 60 and 90. Make sure to write your answer in percent form. Imagine you have two estimators. One of these estimators is unbiased and one has a smaller variance. Explain how you would decide between those two estimators.

Explanation / Answer

a)this is continous random vvariable

c) Area should be 1

hence p*(100 -60) - 1/2*p*((90 - 60) = 1

p(40 - 15) = 1

p = 1/25 = 0.04

c) P(60 <X< 90) =

= 1 - P(X >90)

= 1 - 1/25 * (100 -90)

= 1 - 10/25 = 0.6

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