HW1 - STAT 350 Homework #1 SOLUTION 1. Text problem 1.16...

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STAT 350 – Homework #1 SOLUTION 1. Text problem 1.16 (page 23) 80 70 60 50 40 30 20 10 14 12 10 8 6 4 2 0 IDT Frequency Histogram of IDT 1.8 1.6 1.4 1.2 9 8 7 6 5 4 3 2 1 0 log10(IDT) Histogram of log10(IDT) The original data was positively skewed. The transformed data is much more symmetric and nearly bell-shaped.
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2. X is a discrete random variable with the following PMF: () 2 37 12 if 1,2, ,12 158 0o t h e r w i xx x px ⎛⎞ −+ = ⎜⎟ = ⎝⎠ K s e a. Find P( X = 3) () () 2 37 12 3 3 10 3 0.06329 158 158 p == b. Find P(3 < X < 6) 527 4 5 0.04430 158 158 158 pp =+= + = c. Find P(3 X 6) () () () () 10 5 2 1 18 3 4 5 6 0.1139 158 158 158 158 158 pppp = + + + =+++=≈ 3. Take a standard deck of 52 cards. Shuffle them thoroughly then look at the top card. Put that card back in the deck, shuffle again and repeat this process for a total of 20 times. The number of times the top card is a Queen is a binomial random variable. a. Find the values of the parameters for this random variable ( n and π ) n = 20, = 4/52 b. Find the probability a queen is on top exactly 2 of the 20 times.
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HW1 - STAT 350 Homework #1 SOLUTION 1. Text problem 1.16...

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