Decision Alternative d₁ d₂ States of Nature 51 52 53 240 90 90 15 90 65 Suppose that the decision maker obtained the probabilities P(S₁) = 0.65, P(S₂) = 0.15, and P(S3) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₂) = EV(d₂) = The optimal decision is

X 0.1 0.2 0.3 0.4 0.5 y 0.06 0.12 0.36 0.65 0.95 Formulate a mathematical model that minimizes the largest deviation (Chebyshev Criterion) and between the data and the model P = c₁x² + C₂x + C3. HINT: Perform techniques in Operations Research to solve the problem like Simplex Method.

Two six-sided dice are rolled, and the random variable X is defined as the sum of the two numbers. Fill in the partial pdf for X.

Could you solve (i), (ii)? Thank you.

Part (i) The chance of developing breast cancer is under 11% for women. Ho: M=11, Hg μ#11 Ho: M211, Hg: μ 11 Ho: p=0.11, H₂: P# 0.11 O Ho: Ho: P 20,000, Ο Ηρ: μ 5 20,000, O Ho: p = 20,000, O Ho: p ≤ 20,000, O Ho:p> 20,000, Ho: μ ε 20.000, O Ho: p≥ 20,000, Additional Materials Reading Hg μ 5 20,000 Hg μ > 20,000 Ha: p= 20,000 Hp> 20,000 He: p ≤ 20,000 Hg με 20,000 Ha: p<20,000

1 a and b please thank you!!

Expected value = E(x) = x1P1+x2P2+ ... + xnPn Where x = the outcome and P = probability of outcome Dr. Kimball likes to go fishing with his son. To motivate his son, he pays him for the first fish that he catches. There are two types of edible fish that his son can catch: Trout and Salmon.  If he catches a Trout he pays him $5, if he catches Salmon $3. There is a 20% chance that he will catch a trout and 50% that he will catch a Salmon.

Linearity of expectations. A class with 11 third graders and 9 fourth graders are lined up in a random order for recess. T is the random variable which is equal to the number of 3rd graders in the first 3 places of the line. What is the expected value of T? E[T] = Ex: 1.23