3. (15 points). You flip a rigged coin 3 times with Pr(Head)...

3. (15 points). You flip a rigged coin 3 times with Pr(Head) = 0.2 and the random variable X is the number of Heads. Note that S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} a. Please workout and draw the probability distribution of the random variable X. b. Calculate the mean and variance of X. c. What is the probability that the random variable X takes on a value of 2 or more?

Transcript

00:01 In this question we're given that a coin is rig.

00:04 Probability of getting a head in a toss is 0 .2.

00:07 So probability of getting a tail will be 1 minus probability of getting a head.

00:13 And so probability of getting a tail will be 0 .8.

00:18 Now you flip the coin three times, and the random variable x is the number of heads out of the three tosses.

00:26 I'm going to let event h be a head appears in a toss, and t be a tail appears in a toss.

00:32 And as is the entire sample space, it consists of all the possible outcomes.

00:39 In part a, we want to find the probability distribution of the random variable x.

00:45 Now, take note that we have three trials here, since the coin is tossed three times.

00:49 So, n, the number of trial is three.

00:52 And p, probability of success in a single trial, and there is probability of getting a hay in a toss, and that will be 0 .2.

01:00 So this is probability of event h and this is probability of event.

01:10 So x follows the binomial distribution.

01:14 N is 3, p is 0 .2.

01:18 So probability x equals to r, where r is the number of success, out of n trials, in this case, is the number of heads out of three tosses.

01:31 And that will be three choose r, 0 .2 to the power r and 1 minus 0 .2 will be 0 .8 to the power 3 minus r.

01:40 Now i'm going to draw the probability distribution table here.

01:45 This is r and this is probability x equals to r.

01:49 Now possible values for r will be 0, 1, 2, 3...

Question

Please give Ace some feedback