X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1. b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2. c) Find the expected value of the random variable X1. d) Find the expected value of the random variable X2. e) Find the variance of the random variable X1. f) Find the variance of the random variable X2. g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability. h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability. i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is below
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass
a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.
b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.
c) Find the
d) Find the expected value of the random variable X2.
e) Find the variance of the random variable X1.
f) Find the variance of the random variable X2.
g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.
h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.
i) Are the random variables X1 and X2 independent? Show it.
The combined probability mass function of the random variables X1 and X2 is below
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