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- F(x) is cdf of X. Cumulative probability X is 2,4,7 and 9 is 0.1,0.4,0.8 and 1. calculate the probability if more than fiveGiven the probability density function f(x)=14f(x)=14 over the interval [2,6][2,6], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation:The pH water samples from a specific lake is a random variable X with probability density function. f(x) = {8 (7– x)², 5 < x<7 0, elsewhere a. ) Find E(X) ( expected value or mean) b. ) Find V(X) ( Variance)The standard normal probability function is used to describe many different populations. Its graph is the well-known normal curve. A related function is defined below. Give the intervals where the function is increasing and decreasing. Is your answer geometrically obvious? f ( x ) = 1 / sqrt ( 4π ) e -x^2 / 3Suppose that the length of a phone call in minutes follows exponential distribution with parameter λ=8. If some one comes ahead of you in queue of telephone booth, then find the probability that you have to wait between 10 and 20 minutes.Given the probability density function f(x)=15f(x)=15 over the interval [3,8][3,8], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation2.A card is randomly selected from a deck of 52 playing cards, find the probability that it is I) A back card or an Ace ii) Queen of spade.Given the probability density function f(x)=13f(x)=13 over the interval [4,7][4,7], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation:Given the probability density function f(x)=14f(x)=14 over the interval [3,7][3,7], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation:The standard normal probability function is used to describe many different populations. Its graph is the well-known normal curve. This function is defined below. Give the intervals where the functions is increasing and decreasing. f(x) = 1 -x²14 √3xSEE MORE QUESTIONS