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)© BrainMass Inc. brainmass.com December 15, 2022, 7:58 pm ad1c9bdddf
Solution to Q1.
(a) To find c, we need to use the property . So,
Integrating it, we have
(b) To find CDF, we need to compute F(x)= . We discuss two ...
The probabilities and statistics for a random variable is determined.