Chapters

Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
Solution of exercise 4
Solution of exercise 5
Solution of exercise 6

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Exercise 1

A pair of a die is thrown. The random variable, X, is defined as the sum of the obtained scores. Determine the probability distribution, the expected value, and variance.

Exercise 2

A player throws a die. If a prime number is obtained, he gains to win an amount equal to the number rolled times 100 dollars, but if a prime number is not obtained, he loses an amount equal to the number rolled times 100 dollars. Calculate the probability distribution and the expected value of the described game.

Exercise 3

The first prize for a raffle is 5,000 dollars (with a probability of 0.001) and the second prize is 2,000 dollars (with a probability of 0.003). What is a fair price to pay for a single ticket in this raffle?

Exercise 4

Let X be a discrete random variable whose probability distribution is as follows:

$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$

1. Calculate the distribution function.

2. Calculate the following probabilities:

$\text{[math]}$

Exercise 5

A player tosses two coins into the air. He wins 1 dollar for the number of heads he will get. However, he will lose 5 dollars if neither coin is a head. Calculate the expected value of this game and determine whether it is favorable for the player.

Exercise 6

Knowing that $\text{[math]}$ and $\text{[math]}$ . Calculate:

1. The expected value.

2.The variance.

3.The standard deviation.

Solution of exercise 1

A pair of die is thrown. The random variable, X, is defined as the sum of the obtained scores. Determine the probability distribution, the expected value and variance.

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
		$\text{[math]}$	$\text{[math]}$

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 2

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
		$\text{[math]}$

$\text{[math]}$

Solution of exercise 3

$\text{[math]}$

$\text{[math]}$ dollars

Solution of exercise 4

Let X be a discrete random variable whose probability distribution is as follows:

$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$

$\text{[math]}$

1. Calculate the distribution function.

2. Calculate the following probabilities:

$\text{[math]}$

Solution of exercise 5

$\text{[math]}$

Probablity of getting 1 head= $\text{[math]}$

Probablity of getting 2 heads= $\text{[math]}$

Probablity of getting two tails= $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

Hence, it is unfavorable.

Solution of exercise 6

Knowing that $\text{[math]}$ and $\text{[math]}$ . Calculate:

1. The expected value.

2.The variance.

3.The standard deviation.

$\text{[math]}$

After solving the above equations simultaneously, the value of a will be "0 " and the value of b will be "0.45".

$\text{[math]}$

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
		$\text{[math]}$	$\text{[math]}$

$\text{[math]}$

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vikhyat

January 2023

In question 3 : i think you have missed 9 . it should be (10*9)/2 (1/5)^2(4/5)^8

rajjaa

April 2022

good job

Christopher

February 2022

Can you give me 5 real-life problems involving random variables?
i need it now please

malek

November 2021

A) 0.2668
B) 0.33965
C) 0,04575
D) 0.97175

Alice Kazoozu

October 2021

Hello please
Can you please help me with question 6?
Thank you

Sajeethan

July 2021

CORRECTION

p (AUB) = 0.05 + ( (1 – 0.05 ) x 0.1) = 0.145

in 6th question a part

Toyin

February 2022

Pls explain question six 2

Dhairya

April 2021

For ex.2 part.3 there’s a rounding error – the answer is 0.165

Promise

August 2021

Please help me work these cumulative binomial probability.
In a particular strain of staphylococcus product abdominal cramps in 30% of person infected. At a clinic 10 persons ate contaminated food and were infected with the organisms, find:
A) exactly three people will develop the symptoms.
B) between 3 and 7 inclusively will develop the symptoms.
C) more than 5 people will develop the symptoms.
D) at least one person will develop the symptoms.

malek

November 2021

A) 0.2668
B) 0.33965
C) 0,04575
D) 0.97175

Expected Value Word Problems

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Solution of exercise 6

Random Variable

Binomial Distribution

Distribution Function

Expected Value

Binomial Coefficient

Discrete Probability Distributions