8) The probability density function of a particular...

8) The probability density function of a particular continuous random variable x is described in the graph below. Determine the following. a) $P(x > 4)$ b) $P(2 < x < 6)$ c) $P(x < 5)$ d) $P(x > 8)$

Transcript

00:01 And ask a question we have the following dynasty function.

00:07 F of x equals 0 .4 minus 0 .1 x when x is between 0 and 4 and 0 .1 x minus 0 .4 when x is between 4 and x and of course it's 0 else else where x is between 4 and x and c and of course it's 0 elsewhere the first requirement is to graph the density function.

00:48 To make the graph, we notice that x is only positive values starting from 0, and we have a change in 4 and we have value of 6 here, then this might be 2.

01:07 This is 2 and this is 6.

01:14 For this interval when x equals 0, you can notice that f of x is 0 .4, and when x equals 2, it is 0 .4, it is 0 .4 minus 0 .2 .2.

01:30 It is 0 .2 when x equals 4 is 0 then it's a line and we can make the equal sign in each one doesn't matter and when x equals 6 we can substitute here it's 0 .1 multiply by 6 minus 0 .4 it's 0 .2 again this is the dynasty function for the random variable x the second requirement is to find the probability that x is lived down the less than 2 x is less than 2 we can find this probability using the graph it is the area under this portion now we can find this area we can divide it into two piece the first piece is this rectangular it is half applied sorry it's the base multiplied by the height the base is 2 minus 0 it's 2 apply by the height it's 0 .2 plus the area of this rectangle it is half by base which is 2 minus 0 .0 by height which is 0 .4 minus 0 .2 it's 0 .2 then the probability of x to be smaller than 2 it's 0 .4 plus 0 .2 it's 0 .6 let's find the probability that x is greater than 5 of x to be greater than 5 it is the area of this part what is this value it is 0 .1 because this is a linear function it starts at 0 .2 then in the middle it's 0 .1 it's divided into two pieces like previous it is it is the base which is 6 minus 5 it's 1 applied by the height it's 0 .1 plus the area of the triangle it's a half by the base 1 by height 0 .2 minus 0 .1 it's 0 .1...

Question

8) The probability density function of a particular continuous random variable x is described in the graph below. Determine the following. a) $P(x > 4)$ b) $P(2 < x < 6)$ c) $P(x < 5)$ d) $P(x > 8)$

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