|A 8 A sequence of independent Bernoulli trials with probability of success p is performed. Let the ran dom variable X be the number of failures before the first success. R.D.R EGALA STAT 203 March 4, 2021 a) Find the probability mass function of X, confirming that the sum over all possible values of X is one.

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|A 8
A sequence of independent Bernoulli trials with probability of success p is performed. Let the
random variable Xbe the number of failures before the first success.
R.D.R EGALA
STAT 203
March 4, 2021
a) Find the probability mass function of X, confirming that the sum over all possible values
of X is one.
b) Obtain E(X)
c) The probability of an enemy aircraft penetrating friendly airspace is 0.01.
i) What is the probability that the first penetration of friendly airspace is accomplished
by the 80th aircraft to attempt the penetration, assuming penetration attempts are
independent?
i) What is the probability that it will take more than 80 attempts to penetrate friendly
airspace?
i) Consider Y, the total number of failures before the second success. Find the probability
mass function of Y. By considering the mean of X, show that
E (Y) = 2|
Transcribed Image Text:|A 8 A sequence of independent Bernoulli trials with probability of success p is performed. Let the random variable Xbe the number of failures before the first success. R.D.R EGALA STAT 203 March 4, 2021 a) Find the probability mass function of X, confirming that the sum over all possible values of X is one. b) Obtain E(X) c) The probability of an enemy aircraft penetrating friendly airspace is 0.01. i) What is the probability that the first penetration of friendly airspace is accomplished by the 80th aircraft to attempt the penetration, assuming penetration attempts are independent? i) What is the probability that it will take more than 80 attempts to penetrate friendly airspace? i) Consider Y, the total number of failures before the second success. Find the probability mass function of Y. By considering the mean of X, show that E (Y) = 2|
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