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

where k is a constant.

a. Find the value of k.

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

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 median reading?

f. What is the standard deviation?

Answer

Step 1 of 6

a)Here we have to find the integration of the given pdf

And that will be equal to total probability one

(1-⅓)-(-1+⅓) =1/k

2-(⅔)=1/k

k=¾

k=0.75