An unfair coin with heads 7 times as likely as tails is...

An unfair coin with heads 7 times as likely as tails is flipped four times. If X is the number of heads flipped, how many distinct values of X are possible? ANS 5 Find the probability density function of X (Note: Please write the values of X in ascending order!).

Transcript

00:01 In this video, our objective is to find out how many distinct values of x are possible.

00:06 All right.

00:07 And the given information is probability of heads is equals to 7 times probability of tails.

00:21 All right.

00:24 And probability of heads plus probability of tails is equals to 1.

00:33 All right.

00:33 Now 8 times probability of tails is going to be equals to 1 now we can say that probability of tails is going to be equals to 1 upon 8 and according to that probability of heads let's find out the probability of heads this is going to be equals to 7 upon 8 since n is the binomial distribution with parameters n is equal to 4 and p is equal to 4 and p is equals to 7 upon 8.

01:07 So here we can use the binomial distribution formula to calculate the, to find out the distinct value of x that are possible.

01:29 So the usual binomial distribution formula is probability of x is equal to n, c, x times p, which is the probability of success to the power x times q, which is 1 minus probability of success, probability of failure to the power n minus x this is the usual formula to find out the binomial probabilities now as we know we can see that the distinct value of x are possible here is x are possible here is 0 1 2 3 4 all right now let's find out the probabilities so the so probability of x is equal to 0 is equal to we'll plug in the formula we'll plug in the values in this given formula distribution formula so this is going to be equals to 1 upon 8 to the power 4 and by using the calculator you can find this value this is equal to 0 .000 to 4 all right now when the probability of x is equal to 1 when the value of x is equal to 1 this is equal to 4 times 7 upon 8 to the power x all right so here the the value of x is 1 times 1 minus 7 upon 8 to the power n minus x all right solving this is equal to 3 this is equal to 3 all right so solving this is equal to 0 .0 .0686 all right now probability of x is equal to that is equals to 4 c2 times 7 7 upon 8 to the power 2 times 1 minus 7 upon 8 to the power 2 and solving this side this is equal to 0 .071777 all right now probability of x is equal to 4 3 we'll do up to 4 okay so 4 times 7 upon 8 to the power 3 times 1 minus 7 7 7 upon 8 that is equals to 0 .334961...

Question

An unfair coin with heads 7 times as likely as tails is flipped four times. If X is the number of heads flipped, how many distinct values of X are possible? ANS 5 Find the probability density function of X (Note: Please write the values of X in ascending order!).

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