Joint and Marginal Probability Mass Function

IMPORTANT

Joint and Marginal Probability Mass Function: Overview

This Topic covers sub-topics such as Joint Probability Mass Function, Marginal Probability Mass Function and, Joint and Marginal Probability Density Function

Important Questions on Joint and Marginal Probability Mass Function

EASY

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 1

If the joint probability mass function of two discrete random variables $X$ and $Y$ is $P_{X Y} (x, y)$ which is given by

	$Y = 0$	$Y = 1$
$X = 0$	$\frac{3}{8}$	$\frac{1}{4}$
$X = 1$	$\frac{1}{8}$	$\frac{1}{4}$

Find the marginal probability mass function of $X$ .

EASY

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 2

If the joint probability mass function of two discrete random variables $X$ and $Y$ is $P_{X Y} (x, y)$ which is given by

	$Y = 0$	$Y = 1$
$X = 0$	$\frac{1}{8}$	$\frac{3}{8}$
$X = 1$	$\frac{1}{4}$	$\frac{1}{4}$

Find the marginal probability mass function of $Y$ .

EASY

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 3

If the joint probability mass function of two discrete random variables $X$ and $Y$ is $P_{X Y} (x, y)$ which is given by

	$Y = 0$	$Y = 1$
$X = 0$	$\frac{1}{8}$	$\frac{3}{8}$
$X = 1$	$\frac{1}{4}$	$\frac{1}{4}$

Find the marginal probability mass function of $X$ .

EASY

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 4

If the joint probability mass function of two discrete random variables $X$ and $Y$ is $P_{X Y} (x, y)$ which is given by

	$Y = 0$	$Y = 1$
$X = 0$	$\frac{1}{4}$	$\frac{1}{4}$
$X = 1$	$\frac{1}{8}$	$\frac{3}{8}$

Find the marginal probability mass function of $Y$ .

MEDIUM

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 5

The joint probability density function ̥of two discrete random variables $X, Y$ is $f (x, y) = {\begin{array}{cl} x^{3} y^{2}, & 0 \leq x \leq 1, 0 \leq y \leq 1 \\ 0, & elsewhere \end{array}$ , then the marginal probability density function of $X$ is

MEDIUM

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 6

The joint probability density function ̥of two discrete random variables $X, Y$ is $f (x, y) = {\begin{array}{cl} x y^{2}, & 0 \leq x \leq 1, 0 \leq y \leq 1 \\ 0, & elsewhere \end{array}$ , then the marginal probability density function of $X$ is

EASY

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 7

The joint probability mass function of two discrete random variables $X$ and $Y$ is given by

$Y \to$	$1$	$3$	$9$
$\underset{↓}{X}$	$1$	$3$	$9$
$2$	$0.1$	$0.1$	$0.05$
$4$	$0.2$	$0$	$0.1$
$6$	$0.1$	$0.15$	$K$

Find $K$ .

MEDIUM

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 8

The joint probability density function ̥of two discrete random variables $X, Y$ is $f (x, y) = {\begin{array}{cl} x^{2} y, & 0 \leq x \leq 1, 1 \leq y \leq 2 \\ 0, & elsewhere \end{array}$ , then the marginal probability density function of $X$ is

EASY

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 9

If the joint probability mass function of two discrete random variables $X$ and $Y$ is $P_{X Y} (x, y)$ which is given by

	$Y = 0$	$Y = 1$
$X = 0$	$\frac{1}{4}$	$\frac{1}{4}$
$X = 1$	$\frac{1}{8}$	$\frac{3}{8}$

Find the marginal probability mass function of $X$ .

MEDIUM

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 10

If $X$ and $Y$ be the random variable with their marginal density function as $f (x) = {\begin{cases} 2 x, & 0 \leq x \leq 1 \\ 0 & otherwise \end{cases}$ and $g (y) = {\begin{cases} 2 y, & 0 \leq x \leq 1 \\ 0 & otherwise \end{cases}$ , then $E (X) + E (Y) =$

MEDIUM

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 11

The join probability density function ̥of $X, Y$ is $f (x, y) = {\begin{array}{cl} x^{2} y, & 0 \leq x \leq 1, 0 \leq y \leq 2 \\ 0, & elsewhere \end{array}$ . Then the marginal probability distribution of $X$ is

HARD

IMPORTANT

mathematics>Random Variables and Mathematical Expectation>Joint and Marginal Probability Mass Function> Q 12

The value of $E (3 X)$ $+ E (4 Y)$ for the following joint probability distribution function of $X$ and $Y$ is

$Y \to$	$1$	$2$	$3$
$\underset{↓}{X}$	$1$	$2$	$3$
$- 5$	$0$	$0.1$	$0.1$
$0$	$0.1$	$0.2$	$0.2$
$5$	$0.2$	$0.1$	$0$

Joint and Marginal Probability Mass Function

Joint and Marginal Probability Mass Function: Overview

Important Questions on Joint and Marginal Probability Mass Function

Learn and Prepare for any exam you want !