Let f(x) = k(5x − x²) if 0 ≤ x ≤ 5 and f(x) = 0 if x < 0 or x > 5. - (a) For what value of k is f a probability density function? k = (b) For that value of k, find P(X > 1). P(X > 1) = (c) Find the mean. μ =
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- A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?If probability density function of a random varíable X is f(x) = x² for –1SXS1, and %3D O for any other value of x %3D is then, the percentage probabilityPSuppose that therandom variable X has the probability density function c(1– x2) for -1s x <1 f(x) elsewhere What is the variance of X
- Q1Suppose Uniform(01,02) where the parameters 01 and 02 take the values -4 and -3 respectively. Compute the probability P(Y < y) when y=-3.90.Consider the three functions I. f(x)= {1-x if 0 < x < 2 {0 otherwise II. f(x)= {1+x if 0 < x < 2 {0 otherwise III. f(x)= {(3/27)x^2) if 0< x < 3) {0 otherwise Which of these above functions can be probability distributions? And why?
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