Chapters

## 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.

The best Maths tutors available
4.9 (36 reviews)
Intasar
£48
/h
1st lesson free!
4.9 (28 reviews)
Paolo
£30
/h
1st lesson free!
4.9 (23 reviews)
Shane
£25
/h
1st lesson free!
5 (16 reviews)
Jamie
£25
/h
1st lesson free!
5 (17 reviews)
Matthew
£30
/h
1st lesson free!
4.9 (12 reviews)
Petar
£40
/h
1st lesson free!
4.9 (17 reviews)
Farooq
£40
/h
1st lesson free!
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
4.9 (36 reviews)
Intasar
£48
/h
1st lesson free!
4.9 (28 reviews)
Paolo
£30
/h
1st lesson free!
4.9 (23 reviews)
Shane
£25
/h
1st lesson free!
5 (16 reviews)
Jamie
£25
/h
1st lesson free!
5 (17 reviews)
Matthew
£30
/h
1st lesson free!
4.9 (12 reviews)
Petar
£40
/h
1st lesson free!
4.9 (17 reviews)
Farooq
£40
/h
1st lesson free!
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!

## 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:

1. Calculate the distribution function.

2. Calculate the following probabilities:

## 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 and . 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.

## Solution of 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.

## Solution of 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?

dollars

## Solution of exercise 4

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

1. Calculate the distribution function.

2. Calculate the following probabilities:

## Solution of 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.

Probablity of getting 1 head=

Probablity of getting 2 heads=

Probablity of getting two tails=

Hence, it is unfavorable.

## Solution of exercise 6

Knowing that and . Calculate:

1. The expected value.

2.The variance.

3.The standard deviation.

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

The platform that connects tutors and students

Did you like this article? Rate it!

4.00 (3 rating(s))