function P(x) Csin(x)y, for 0 ≤ x ≤ and 1 ≤ y ≤ 2 h value of C is P(x) a joint probability density function for X and Y? ad Y independent random variables? Justify.
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- A random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.* Consider the probability density function fx (x) = a e-b lel where X is the random %3D variable which assumes all the values from (i) relation between a and b -00 to -00, Find (ii) the probability of finding X in the range 1 to 2.c) A continuous random variable X takes values in the interval 1 < x < 3and the probability density function of x is given by: k f(x) (i) (ii) Plot the pdf of the X Show by calculation how you can determine the value of K, the expected value and the variance
- Q/ Let it be the probability density function n-x [") ³²-1"-² ax Let it be Y = e x = 0, 1, 2, So, E(Y) is ?function given by Suppose that X and Y have a joint probability density 7e-2-7y if x, y ≥ 0 otherwise fxy(x, y) = = (d) Are the random variables X and Y independent? Justify your answer.continuous random variable has probability density function given by F(x) =k(2x+3) 1<=x<=2 0 ,otherwise Find k if f(x) is a probability density functionFind Value of k P(1.5<=x<=4) ?
- The probability distribution functions (discrete random variable) or probability density functions (continuous random variable) for a random variable X are (b) (c) f (x) = c exp (- 6 x) x > 0 - 1 0 ƒ(x)=c()*, x = 0, 1, 2,... Find C.Question: What is the variance of a continuous random variable Y with probability density function (pdf) given by g(y) = 4y^3, 0 < y < 1?A continuous random variable X has probability density function f given by (kx* (4-x) for 0sx54 f(x)={ elsewhere Find (a) the value of k. (b) the mean and variance of X. (c) P(lFigure I shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function F(x) for continuous random variable. F(x) (6. 1) IV III II (4.0.8333) (0.0.1667) Figure I Construct the probability density function fix). Should one of the piecewise functions (IV) is not constant, explain the changes.Sizes of insurance claims can be modeled by continuous random variable X with probability density f(x) = c(10 - x) for 0 < x < 10 and f(x) = 0 otherwise, where c is some constant. What is the value of c? What is the probability that the size of a particular claim is no more than 5 and what is the probability that the size is more than 2?The joint probability density function of two random variables X and Y is given by f(x, y) = Ja (2x + y?) 0 3)SEE MORE QUESTIONS