00:01
So here we have x, our random variable, is the number of watchers in the sample who prefer leno that would be distributed as a binomial random variable with the number of trials being equal to 3 and the probability of somebody preferring j.
00:17
Leno being 0 .52.
00:20
So for the probability distribution, we know that the probability that x equals a particular value should be equal to 3 choose x times 0 .52 to the power of x times 1 minus 0 .52 or 0 .48 to the power of 3 minus x.
00:42
So what i'm going to do is i'm just going to pull up my preferred software for doing these calculations.
00:48
Create a little table here.
00:50
So i'll have my x value and then binomial 3x.
00:55
That's the 3 choose x thing 0 .52 of x 0 .48 3 minus x do that for x between 0 and 3 and 3 and i'll just get this displayed as a table so we have that this would be reflective of our oh actually just going to round these values to let's say 3 decimal places that to 3 decimal places just to make it a little bit easier to work with.
01:31
And so now what i'll do is just copy this into my one note here.
01:36
So we have x equal 0, 1, 2, and 3.
01:39
And then p of x, 0 .11, 0 .159, 0 .359, 0 .389, and 0 .141.
01:51
So that is our probability distribution.
01:54
Then for part b, the probability histogram, that would be relatively straightforward to do here.
02:03
So, actually, what i'll do is i'll pull up excel, that is remnant from a previous problem.
02:09
So we have x, e of x, 012, and 3, and what were the values? they were 0 .111, 0 .359, 0 .389, and 0 .141.
02:31
That adds up to one.
02:33
And for the histogram, we'd actually want to insert a bar chart here, where it's not quite interpreting this correctly.
02:44
So let's see here, chart design, select data.
02:48
We want one series, that is the p of x, with the horizontal axis labels, should be 0, 1, 2, and 3...