Need help with this PMF word problem. Will rate life saver. \"In college basketb

Question

Need help with this PMF word problem. Will rate life saver.
"In college basketball, when a player is fouled while not inthe act of shooting and the opposing team is "in the penalty," theplayer is awarded a "1 and 1." In the 1 and 1, the player isawarded one free throw and if that free throw goes in the player isawarded a second free throw. Find the PMF of Y, the number ofpoints scored in a 1 and 1 given that any free throw goes in withprobability p, independent of any other throw."
"In college basketball, when a player is fouled while not inthe act of shooting and the opposing team is "in the penalty," theplayer is awarded a "1 and 1." In the 1 and 1, the player isawarded one free throw and if that free throw goes in the player isawarded a second free throw. Find the PMF of Y, the number ofpoints scored in a 1 and 1 given that any free throw goes in withprobability p, independent of any other throw."

Explanation / Answer

Let X: then score in a 1 and 1 .
then
P(X=0, i.e scoring 0 ) = probability that the player missesfirst free hit it self = 1-p (given)
P(x=1) = probability that the player scores a goal in firstfree thow and misses the second = (P)*(1-p)
similarly P(x=n) = probability that the player scores a goalin all first n throws and misses the n+1 st one. =pn (1-p)
The probabilities are the pmf s for the question and thegeneral formula for x=n is also above.
Hope this helps.

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