Consider a probability distribution given by the density function

P(z) = C * z^2, 1

Question

Consider a probability distribution given by the density function

P(z) = C * z^2,  1 <= z <= 4
P(z) = 0,        otherwise

The probability that z lies between 2 and 3, i.e., P(2 <= z <= 3) is _________ (rounded off to three decimal places).

Accepted Answer

P(2 <= z <= 3) = 19/63 ≈ 0.301 We have a continuous PDF of the form C*z^2 defined on [1,4]. First we find the normalising constant C by forcing the total area under the curve to equal 1. Then we integrate the PDF from 2 to 3 to get the required probability. This is a straightforward application of normalisation followed by definite integration of a polynomial PDF.

Consider a probability distribution given by the density function P(z) = C * z^2, 1 <= z <= 4 P(z) = 0, otherwise The probability that z lies between 2 and 3, i.e., P(2 <= z <= 3) is _________ (rounded off to three decimal places).