Description of Probabilities and statistics
1. Let f(x) = 2e^(-(x-3)/c), 3 < x < infinity (zero
otherwise) be a p.d.f. of a random variable X.
a. Find c
b. Find the CDF of X and sketch the CDF
c. Compute P(-5 < X < 10)
2. A candy maker produces mints that have a label weight of
30 grams. Assume that the distribution of the weights of these mints is N(30,
2^2).
a. Let X be the weight of a single mint selected at random
from the production line. Find P(X > 32).
b. Suppose that 20 minutes are selected independently and
weighted. Let Y equal the number of these mints that weigh less than 30 grams.
Then find P(Y = 3).
c. Now, suppose that n = 100 mints are selected
independently and weighted. Let Y equal the number of these mints that weigh
less than 30 grams. Find the probability P(20 < Y <= 30) approximately.
(Hint: Use CLT)
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