Question 2 10 marks i the continuous random variable x has...

Name: question 2 10 marks i the continuous random variable x has probability density functionfxx kx22 0 le x le 2 determine p0 le x le 1 6 ii the number of days that elapse between the beginning 71873
Uploaded: 2024-07-30T23:40:22-08:00
Duration: 4 min 56 s
Channel: Adi S
Description: question 2 10 marks i the continuous random variable x has probability density functionfxx kx22 0 le x le 2 determine p0 le x le 1 6 ii the number of days that elapse between the beginning 71873

Question 2 (10 marks) (i) The continuous random variable $X$ has probability density function:$f_X(x) = k(x+2)^2, 0 \le x \le 2$. Determine $P(0 \le x \le 1)$. [6] (ii) The number of days that elapse between the beginning of each calendar year and the moment a high-risk driver is involved in an accident is exponentially distributed. An insurance company expects that $30\%$ of high-risk drivers will be involved in an accident during the first $50$ days of a calendar year. Calculate the portion of high-risk drivers are expected to be involved in an accident during the first $80$ days of a calendar year. [4]

Transcript

00:01 So we are given according to first part of this question.

00:07 The battery failure time of aptity density function, f of x is equal to 2 by x plus 1 whole cube for x greater than equals to 0 and f of x is equal to 0 for x less than to 0.

00:26 So we need to show that this is a valid probability density function, that is pdf.

00:36 So let's get static to solution.

00:38 So first of all, let me define here the concept.

00:41 Why would we call this as pdf? it will be pdf only if it satisfies the first condition if of x greater than equals to zero for all the values of x.

00:53 One thing and the second most important thing integration with respect to x of x x t x this is should be equals to one only not greater than to x so let's prove these two things we will get to prove it the given thing is the thing that you have pdf so let's prove the first thing so now this we have to prove for x greater than to zero so let's say the function if of x is a two bar x plus 1 of whole cube this is definitely going to be greater than to 0 why because we can just verify it by substituting the value of x let's say f of 1 so this will be goes to 2 by 1 plus 1 of whole cube so 2 that means 1 by 4 okay because 1 2 is get cancer so yes it is satisfying the condition that f of x will be greater than equals to 0 for all x greater than to 0 only for x greater than 0 because if you put x as minus of 1 see that in the answer now if you put negative of 2 so it will become negative so it is only possible when x will be greater than to 0 means f of x will be greater than equal to 0 positive only when x will be positive so this first test is verified now let's check it out the second test.

02:27 What we have stated, the integral f of x d x with respect to x, this should be equals to 1.

02:34 So let's find it out whether it's coming or not.

02:38 So we don't know what is the limit for x.

02:42 Right, so can take its varying from 0 to infinite...

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