Question

For probability density function of a random variable X, P(X < a) can also be described as:

F(a), where F(X) is the cumulative distribution function.

1- F(a) where F(X) is the cumulative distribution function.

The area under the curve to the right of a.

The area under the curve between 0 and a.

Answer 1

For probability density function of a random variable X, P(X < a) can also be described as:

F(a), where F(X) is the cumulative distribution function.

The area under the curve to the right of a = P( X > a)

P( X > a) = 1 - P( X < a)

P( X > a) = 1 - F(a)

The area under the curve to the right of a = 1 - F(a)

The area under the curve between 0 and a.

P( 0 < X < a) = P( X < a ) - P( X < 0 )

P( X < a ) = F(a)

P( X < 0 ) = F(0)

P( 0 < X < a) = F(a) - F(0)

The area under the curve between 0 and a = F(a) - F(0)