The PDF of a continuous random variable X with a triangular...

The PDF of a continuous random variable X with a triangular distribution is given by: f(x) = { 4x if 0 <= x <= 0.5 4 - 4x if 0.5 < x <= 1 0 otherwise. Write down the CDF and then determine P{0.2 < X <= 0.6}.

Transcript

00:01 Hi, i'm david and i'm hitching.

00:02 Have you answering your question? now let me pick up your question here.

00:06 In the question here, we're given the bdf of the random robot x.

00:10 And from here, want to find the cdf.

00:14 Let me remind you that the cdf, denoted by the capital of the x, and then it just equal to the probability of the x more equal to the small x.

00:25 And for the continuous random variable, this probability just equal to integral 4 minus in point, infinity up to the x, fx, d x.

00:35 Now here let's try to consider the first interval for x between the interval from 0 to 0 .5 and then the fx is equal to integral.

00:47 For this interval we will have the 0 up to the x, then we have the form.

00:52 Instanwriting the x here we will convert to the order, the variable will be t d t.

00:57 And an antide derivative will be the 2t square or 2t square, evaluate from 0 to the x.

01:05 Then we get equal to the 2x square for the x inside the interval from the 0 to 0 .5.

01:14 And then let's move on to the x inside the interval from the 0 .5 to 1.

01:25 And then the capital of the f now it will equal to integer.

01:28 From the 0 up to the 0 .5 40 d t plus from the 0 .5 up to the x because now x will be in the second interval and the second interval we will have the function is of the form 4 minus 40 d t for the first the degree to get the first integral here get equal to the 2 t square add the 0 to the 0 .5 plus the second one entirely derivative could be the 4 t minus 2 t square evaluating at the 0 .5 up to the x and it will simplify it we get equal to and the 0 .5 we got the 2 and then 1 out of 4 and this will be plus the we're looking at x we got the 40 and then 4 x minus 2 x square and then we minus the 4 times 0 1 5 will be 2 and this one plus the 2 10 with the 1 out of 4 and it will simplify this one again equal to the 2 times 1 at the phone would be a half so it will be minus 1 so we have the 4 x minus 2 x square minus 1 and that's will be the density, the cdf, so we can recap everything here...

Question

The PDF of a continuous random variable X with a triangular distribution is given by: f(x) = { 4x if 0 <= x <= 0.5 4 - 4x if 0.5 < x <= 1 0 otherwise. Write down the CDF and then determine P{0.2 < X <= 0.6}.

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