I need solve this question of IE230-Probability and Statistics in Eng. I

Instructions for choosing your personally assigned data for Assignment 2 For Question 1 you will need your personally assigned probability density function f(x) and range Rx to solve the question. Variance (62) Function Probability density function f(x, nd for solving range Rx equal 7 3 Less than or f ( x ) = 256 (8x - x2), Rx: 0S x58 50 equal to 7 3 f (x) = (6x - x2), Rx: 0 S x56 More than 108 75 Question 1. Continuous Probability Distributions [55 points] Let X denote the time until recharge for a battery in a laptop (in minutes). The probability density function of X is f(x), XER Use your personally assigned function f(x) and range Rx to answer the following questions. (a) Show that f(x) is a probability density function. [5 points] (b) Find the probability P(X > 4). [10 points] (c) Find the probability P(1.5 4 J. [10 points] (c) Find the probability Pr 1.5