Mathematics > QUESTIONS & ANSWERS > CS 70 Discrete Mathematics and Probability Theory Course Notes With Solutions | Download for quali (All)
CS 70 Discrete Mathematics and Probability Theory Course Notes With Solutions | Download for quality grades | 100% correct answers
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1 Head Count Consider a coin with P(Heads) = 2/5. Suppose you flip the coin 20 times, and define X to be the number of heads. (a) Name the distribution of X and what its parameters are. (b) What i ... s P(X = 7)? (c) What is P(X ≥ 1)? Hint: You should be able to do this without a summation. (d) What is P(12 ≤ X ≤ 14)? Solution: (a) Since we have 20 independent trials, with each trial having a probability 2/5 of success, X ∼ Binomial(20,2/5). (b) P(X = 7) = 20 7 2 5 73 5 13 . (c) P(X ≥ 1) = 1−P(X = 0) = 1− 3 5 20 . (d) P(12 ≤ X ≤ 14) = P(X = 12) +P(X = 13) +P(X = 14) = 20 122 5 123 5 8 + 20 132 5 133 5 7 + 20 142 5 143 5 6 . 2 Exploring the Geometric Distribution Suppose X ∼ Geometric(p) and Y ∼ Geometric(q) are independent. Find the distribution of min{X,Y} and justify your answer [Show More]
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