Suppose that random variable X is uniformly distributed between 5 and 22. Draw a graph of the density function, and then use it to help find the following probabilities: A. P(X> 22) = B. P(X 13.1) =

For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 36) f(x)== // [12, 20] 36) B) μ = 16; o² = 5.33; o = 2.31 A) μ = 15.5; o2=5.20; o = 2.28 C) μ = 15; o2 = 5.34; o = 2.31 D) μ= 1.6; o2 = 5.24; o=2.29

2. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs 2 S (v) . else What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density а. function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: Find?(r - 1.5)) = 1 CO0

Consider hourly wages, letting x be an individual's wage and assuming that wages in the population follow a continuous uniform distribution, ranging from the lowest value of $11 to the highest value of $36.  Please answer each of the following: Write down the probability density function,  f(x) for the random variable x . Compute P(x<14) Compute P(20<x<30) Compute P(x>34)