(a) Find P{X=2}
(b) Find P{X<2}
(c) Find P{2 <= X < 2.5}
Solution:
(a) Find P{X=2} (b) Find P{X<2} (c) Find P{2 <= X < 2.5} The cumulative distribution...
4.3.2 The cumulative distribution func- tion of random variable X is 0 r<-1, Fx (x) = (z + 1)2-1 x < 1, r1 Find the PDF fx(a) of 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)
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
2. The cumulative distribution function of X is given by 0, <0 을, 1 x<2 1O 3 < 3.5 107 1 3.5 Is X a discrete or continuous random variable? Give the appropriate probability mass or density function of X based on your answer.
he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x) is defined by F(x) P(X < x). Example: Suppose the random variable X has the following probability distribution: 123 45 fx 0.3 0.15 0.05 0.2 0.3 Find the cdf for this random variable
Simple Probability Question,
Please explain with details, thank you so much.
Suppose that the cumulative distribution function of the discrete random variable X is given by x V < 0 1L F(x) = { 1 +71 051 x < 2 1 VI Find P{X = 1}, P{X = 2}, P{X = 3} o 1, 11,1 OZ, ÉS 0 ];j; oh, o 12 Find P (} < X < ;) оооо Consider the following two functions S c(2x – 2y) 0...
Question 13 The cumulative distribution function of X is given by Fx (x) = {-kr <0 0<x<2 > 2 Find (a) the value of k, (b) the probability density function fx (x), (c) the median of X, (d) the variance of X.
4. A mixed random variable X has the cumulative distribution function: (0. for x < 0.4 X2 – 0.02 for 0.4 < x < 0.5 Fx(xx) = { 0.2.x3 + 0.6x + 0.25 for 0.5 < x < 0.7 for x > 0.7 (a) Calculate the mean and standard deviation of X. (b) Find P(0.44 < X < 0.62).
Let X be a random variable with the following cumulative distribution function (CDF): y<0 (a) What's P(X < 2)? (b) What's P(X > 2)? c)What's P(0.5 X < 2.5)? (d) What's P(X 1)? (e) Let q be a number such that F(0.6. What's q?
Exercise 3.37. Suppose random variable X has a cumulative distribution function F(x) = 1+r) 720 x < 0. (a) Find the probability density function of X. (b) Calculate P{2 < X <3}. (c) Calculate E[(1 + x){e-2X].