Question

The profit of a market ranges between 400 and 700 Dollar everyday and follows a

uniform distribution. What is :

1. The probability between 200 and 500 Dollar

2. The probability the profit is greater than 400 Dollar

3. The expected value of the profits

Answer 1

Uniform distribution,

If X follows a Uniform(a,b) then

Probability density function of X is given by

Mean of uniform distribution :

X : The profit of a market

X ranges between 400 and 700 dollars everyday and follow a uniform distribution .

i.e X follows Uniform(400,700)

Probability density function of X is given by

1 .The probability between 200 and 500 Dollar = P(200x500)

As the support of x is 400 and 700;

P(200x500) = P(200x<400) + P(400x500)

P(200x<400) = 0

2.

The probability the profit is greater than 400 Dollar = P(X>400)

As given, profit of a market ranges between 400 and 700 Dollar everyday , minimum profit is 400; Therefore,

P(X>400) =1

Anyhow

P(X>400) = 1

3.The expected value of the profits

The expected value of the profits = 550