Problem 2: The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by f(x) = ( C x2 x > 12 0 x ≤ 12 (a) Find the constant C and P(X > 20). (b) What is the cumulative distribution function of X? (c) What is the probability that of 6 such types of devices at least 3 will function for at least 15 hours? What assumptions are you making? (d) Let Y be the lifetime of the same device measured in minutes. What is the probability density function of Y ?

Koji is installing a rectangular window in an office building. the window is 823 feet wide and 534 feet high. the formula for the area of a rectangle is a=bh. what is the area of the window? enter your answer as a mixed number in simplest form in the box. $$ ft2

Kendra had twice as much money as kareem. kendra later spent $8 and kareem earned $6. by then,the two had the same amount of money. how much money did each have originally?

Agroup of student volunteers participates in a study designed to assess several behavioral interventions for improving output in a repetitive task. prior to the beginning of the study, all volunteers unknowingly observed, and their output is measured. at the beginning of the study, prior to any intervention, the volunteers perform the same task under the observation of a study administrator, and their overall output increases. which of the following terms describes this phenomenon? a. simpson's paradox b. hawthorne effect are d. novelty effect d. pygmalion effect e. observer-expectancy effect