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Midterm

# 257test1f11.docx

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Department
Statistics
Course Code
STA256H5
Professor
Craig Burkett

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Description
University of Toronto Mississauga Probability and Statistics I STA257H5F 2011 Term Test #1 Aids Allowed:  non­graphing calculator without a text keypad TOO EASY Printed Name: __________________________________________________ Signature: _____________________________________________________ Student Number: ________________________________________________ TA, Muz, Charles or LingLing:_______________________________________ 1. (3 marks)   Events A and B satisfy P(A) = 0.8 and P(B) = 0.4.  What is the smallest possible  value for P(AB)?  You must justify your answer; there are no marks if you simply write a  probability.   Page 1 of 4 2. (10 marks)   The random variable X has probability mass function    x ­1 0 1 2 p(x) 0.2 0.3 0.4 0.1 Answer each of the following questions.  Put your answers in the chart below.  Only answers  in the chart will be marked. a. Find P(X = 1)   b. Find P (X ≤ 1)   c. Find E(X)   d. Find E(X ) 2   e. Var(X)   3. (4 marks)   Spike is not bright.  The probability he passes chemistry is 0.35, the probability  he passes calculus is 0.40 and the probability he passes both is 0.12.   a. Are the events “Spike passes chemistry” and “Spike passes calculus” independent?   Justify your answer. b. What is the probability he fails both courses? Page 2
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