(6 points) The continuous random variable X has cumulative distribution function given by 0 for x...
(6 points) The continuous random variable X has cumulative distribution function given by 0 for0 for 0 < z < 2 for 2 F(z) = 〈 z-4z2 Part(a) Find Var(X), correct to 2 decimal places. Part(b) Find E(X) correct to 2 decimal places. Part(c) Find P(X>) Give your answer as a decimal, correct to 2 decimal places. Part(d) Find E(X), correct to 2 decimal places. Part(e) Find the value of c correct to one decimal place given that E(Xc) 4E(X-c...
5-5: Problem 1 Previous Problem Problem List Next Problem 1 point) The continuous random variable X has cumulative distribution function given by for z0 for z 2 Parta) Two independent observations of X are taken. Find the probability correct to 2 decimal places that one s ss han Part(b) Find the value of q such that P(X).Give your answer as a decimal correct to 3 decimal places Part(c) Find Var(X), correct to 2 decimal places. Part(d) Find the value of...
The cumulative distribution function for a continuous random variable X is given by 0, S 0 F(x) = 1, r 21. (a) Find the density fx for X. (b) Find the mean ? and variance ?2 for X.
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a Inz, a<<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function S(x) for X. (d) Find E(X)
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a F(x) = Inr, asi<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(x > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x) = Cx -x^2, 0<x<1 for some constant C a. What is the value of C? b. Find P(1/3 < X < 2/3) c. Find the median of X. d. What is the expected value of X?
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot...