Consider a binomial distribution with 10 trials. Look at...

Consider a binomial distribution with 10 trials. Look at Table 3 (Appendix II) showing binomial probabilities for various values of $p$, the probability of success on a single trial. (a) For what value of $p$ is the distribution symmetric? What is the expected value of this distribution? Is the distribution centered over this value? (b) For small values of $p$, is the distribution skewed right or left? (c) For large values of $p$, is the distribution skewed right or left?

Transcript

00:01 For this question we consider a binomial distribution with 10 trials, and you are asked to use a certain table for binomial distribution probabilities for different values of p, where p is the probability of success on a single trial.

00:18 And for part a, we're asked for what value of p is the distribution symmetric.

00:25 Now i don't have this table, but i'm going to show you how we can also do this problem in excel.

00:30 So in column a, i have all the possible values that the binomial random variable x can take on when you have 10 trials.

00:38 Any of the integers from 0 to 10.

00:43 We're going to use different values for the probability of success.

00:49 So let's start with 0 .5.

00:50 I happen to know that this is the value that makes the binomial distribution symmetric.

00:56 In column b, we're going to use the binomial distribution function.

01:03 So we select the one highlighted here in blue.

01:06 For the number of successes, i select the cell.

01:09 In column a.

01:10 For the number of trials, enter 10.

01:14 For the probability of success, i'm going to select the value that we have in column d.

01:21 And then for the cumulative argument we enter false, because we want the probability that x is exactly equal to whatever value is in column a.

01:32 One more thing i do is i add a dollar sign before the two.

01:36 So that means when i do that so that when we copy and fill this formula down for all 11 values of x, 0 through 10, it will continue to use cell d2 for our probability or for the value of p.

01:53 So we hit enter.

01:55 So this is the probability that x equals 0 when the probability success is 0.

02:02 We drag the bottom right of the cell down for all possible values of x and we get all probabilities for these 11 different values of x.

02:12 So this gives the distribution of the binomial random variable for 10 trials when the probability of success is 0 .5...

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