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- a. Explain the difference between the method of moment generating function and the method of incarnation to find the probability density function of a random variable b. Let X1, X2, X3 ,,,,, each of them has Poisson distribution with parameter lamda 1, lamda2, lamda3,........ i. Get the probability distribution of Y=X1+X2+....Xn ii. Get the mean and variance of Y c. Y1 and Y2 be a joint probability function as shown below in the screenshot imageU=Y1/(Y1+Y2), Using the method of incarnation (Jacobian), find the probability density function of UThe probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)b) The continuous random variable Y has the following probability density function. Pembolehubah rawak selanjar Y mempunyai fungsi ketumpatan kebarangkalian seperti berikut. Jh(3y² +2) ; -2sys2 0 ; otherwise f(y)={ 1 Show that h=- 24 i. 1 Tunjukkan bahawa h=; 24 ii. Based on the value in part (i), find the cumulative distribution function F(y). Berdasarkan nilai dalam bahagian (i), cari fungsi taburan longgokan F(y).
- 4. Let X be a random variable with cumulative distribution function given by: F(r) = 1 – e-Az. Find the probability density function and so the expected value of variable X.Let f(x) = x for 0 < x < 1. Is f(x) a legitimate probability distribution function (pdf) for a continuous random variable? No, the area under f(x) is not 1 (it is greater than 1). Yes, all criteria for a pdf are satisfied. No, the area under f(x) is not 1 (it it less than 1). No, f(x) is not non-negative.b) A random variable Xhas probability density function. [Cx(1-x), 0≤x≤1 fx(x) = 3 in) Find [x²] 2 i) Find C. ii) Find P CS Scanned with CamScanner 076, elsewhere
- 5. Suppose that X is a discrete random variable with probability density function p(x) = cx², x = 1, 2, 3, 4. (c) Find Var(X). Select one: O a. 18.4 O b. 354 O c. none O d. 342.8a) Suppose that X is a random variable having the following probability density function given by (2(0-x) 02 f(x) = -, x > 0 (0, elsewhere Find the value of c such that an interval from x to cx is a (1- a)100% confidence interval for the parameter 0.A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. (b) Find cov(X, Y). (c) Are X and Y independent? Explain your answer. Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have X = 1 and Y = 0.