u stlatistics for Engineers Final Exam Fri 12/15 Instructions: You may use any n
ID: 3325176 • Letter: U
Question
u stlatistics for Engineers Final Exam Fri 12/15 Instructions: You may use any notes that you like, including electronic notes. Be sure to show all of your work. It is not necessary to simplify your answers 1. (20 pts) Your friend has a six-sided die with weird probabilities. Let X be a random variable representing the value of a die roll. It has probability mass function; (a) What is the probability of rolling an even number? (b) What is the expected value of a die roll? (c) What is the variance of a die roll? (d) If I roll the die and tell you that it is an even number, what is the probability tha fxExplanation / Answer
a) Probability of getting an even number here is computed as:
P(X = 2 ) + P(X = 4) + P(X = 6) = 0.2 + 0.2 + 0.3 = 0.7
Therefore 0.7 is the required probability here.
b) The expected value here is computed as:
E(X) = 0.1*(1 + 3 + 5) + 0.2*2 + 4*0.2 + 6*0.3 = 3.9
Therefore 3.9 is the expected value here.
c) Here first the second moment of X is computed as:
E(X2) = 0.1*(12 + 32 + 52) + 0.2*22 + 42*0.2 + 62*0.3 = 18.3
Therefore, Var(X) = E(X2) - E2(X) = 18.3 - 3.92 = 3.09
Therefore Var(X) = 3.09
d) The full problem is not visible here.
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