If XX is a random variable and Y=g(X)Y=g(X), then YY itself is a random variable. Thus, we can talk about its PMF, CDF, and expected value. First, note that the range of YY can be written as RY={g(x)|x∈RX}.RY=
Consider a discrete random variableXXwith Range(X)=RX(X)=RX. Note that by definition the PMF is a probability measure, so it satisfies all properties of a probability measure. In particular, we have 0≤PX(x)≤10≤PX(x)≤1for allxx, and ...
The joint PMF of two discrete random variables X and Y is given by: What is the probability of P(Y=2.5). Suppose that X_1 and X_2 are random variables with the joint p.m.f. f ( x_1 , x_2 ) = 1 / 6 ( x_1 , x_2 ) = ( 1 , 1 ) 1 / 9 ( x_...
A random variable Y has cdf G_Y (y) = 10y^9 - 9y^{10} on 0 <= y <= 1(a) Calculate the expected value and variance of the random variable Y (b) Calculate E (Y^{-9}). Let X be a discrete random vari...
Suppose random variables X and Y have the joint PMF. Find the marginal PMF of X. Find the PMF if X is a discrete random variable with the CDF F X ( x ) = 0 x < 0 x 5 0 ? x ? 5 1 x > 5. Let X be a discrete random variable with P X...
Remember that, for a random variableXX, we define the CDF asFX(x)=P(X≤x)FX(x)=P(X≤x). Now, if we have two random variablesXXandYYand we would like to study them jointly, we can define thejoint cumulative functionas follows: ...