There are 21 students in a probability & statistics class. Suppose each lecture
ID: 3170375 • Letter: T
Question
There are 21 students in a probability & statistics class. Suppose each lecture a student is chosen at random to be the "Answer Person". Choices are statistically independent from lecture to lecture. There are 13 lectures. Define a random variable X to be the number of times a specific student, we'll call him Evan, is picked to be the "Answer Person" in these 13 lectures. Compute P (X = 4), i.e. compute P (Evan is picked exactly 4 times in 13 lectures). [0.002370] Compute P (X = 0): i.e. compute P (Evan is never picked in 13 lectures). [0.5303]Explanation / Answer
Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
X ~ B(13,1/21)
a.
P( X = 4 ) = ( 13 4 ) * ( 0.04762^4) * ( 1 - 0.04762 )^9
= 0.00237
b.
P( X = 0 ) = ( 13 0 ) * ( 0.04762^0) * ( 1 - 0.04762 )^13
= 0.5303145
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