Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x)...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
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...
math 4. Let X be a random variable with the following cumulative distribution function (CDF): y <0 F(y) (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?
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
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?
Problem 3. Suppose that the cumulative distribution function of a random variable X is given by (o if b < 0 | 1/3 ifo<b<1B 2/3 if isb<2 2.9 1 if2 Sb. 3.9 (a) Find P(X S 3/2). (b) Find E(X) and Var(X). 4.10
4. Cumulative distribution function (cdf) of a random variable X is given by 1t2 2 Find a) Pdf of X and b) ECX3-2 IXI).
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].
FIND THE CUMULATIVE DISTRIBUTION FUNCTION F(x). The pdf f(x) of a random variable X is given by 3 0, else
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)