Problem 1 Suppose we roll a die, let X be the number we get. Suppose the probability mass function p(x) = P(X = x) is such that p(1) = .1, p(2) = .1, p(3) .1, p(4) = .2, p (5) = 2, p(6) = .3. (1) Calculate P(X > 4). Calculate P(X = 6|X > 4). (2) Calculate E(X), Var(X), and SD(X). Plot p(x) in the form of a histogram. Explain intuitively that E(X) is the center and SD(X) is the spread of the histogram. (3) Suppose the reward for x is h(x), and h(1) = $20, h(2) = $10, h(3) = $0, h(4) = $10, h(5) $20, h(6) = $100. Calculate E(h(X)), Var(h(X)) and SD(h(X)). What are the units of = E(h(X)) and Var(h(X))? (4) Suppose h(x): = 2x + 1. Calculate E[h(X)] using the formula Σ, h(x)p(x). Verify that E[h(X)] = 2E(X) + 1. (5) Suppose h(x) = x². Calculate E[h(X)] using the formula E h(r)p(x). Verify that E(X²) > [E(X)]².
Problem 1 Suppose we roll a die, let X be the number we get. Suppose the probability mass function p(x) = P(X = x) is such that p(1) = .1, p(2) = .1, p(3) .1, p(4) = .2, p (5) = 2, p(6) = .3. (1) Calculate P(X > 4). Calculate P(X = 6|X > 4). (2) Calculate E(X), Var(X), and SD(X). Plot p(x) in the form of a histogram. Explain intuitively that E(X) is the center and SD(X) is the spread of the histogram. (3) Suppose the reward for x is h(x), and h(1) = $20, h(2) = $10, h(3) = $0, h(4) = $10, h(5) $20, h(6) = $100. Calculate E(h(X)), Var(h(X)) and SD(h(X)). What are the units of = E(h(X)) and Var(h(X))? (4) Suppose h(x): = 2x + 1. Calculate E[h(X)] using the formula Σ, h(x)p(x). Verify that E[h(X)] = 2E(X) + 1. (5) Suppose h(x) = x². Calculate E[h(X)] using the formula E h(r)p(x). Verify that E(X²) > [E(X)]².
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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![Problem 1 Suppose we roll a die, let X be the number we get. Suppose the probability mass
.1, p(2) = .1, p(3) = .1, p(4) = .2, p(5) = 2,
function p(x) = P(X = x) is such that p(1)
p(6) = .3.
(1) Calculate P(X > 4). Calculate P(X = 6|X > 4).
(2) Calculate E(X), Var(X), and SD(X). Plot p(x) in the form of a histogram. Explain
intuitively that E(X) is the center and SD(X) is the spread of the histogram.
(3) Suppose the reward for z is h(x), and h(1) = -$20, h(2) = -$10, h(3) = $0, h(4) = $10,
h(5) $20, h(6) = $100. Calculate E(h(X)), Var(h(X)) and SD(h(X)). What are the units of
=
=
E(h(X)) and Var(h(X))?
(4) Suppose h(x)
E[h(X)] = 2E(X) + 1.
(5) Suppose h(x) = x². Calculate E[h(X)] using the formula E h(r)p(x). Verify that E(X²) >
[E(X)]².
=
2x + 1. Calculate E[h(X)] using the formula E h(x)p(x). Verify that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6636eb33-42d6-4272-bfea-d1fbe996ff30%2F45309288-7bbe-4996-a9a9-c6547882960e%2Fpx0gu7w_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1 Suppose we roll a die, let X be the number we get. Suppose the probability mass
.1, p(2) = .1, p(3) = .1, p(4) = .2, p(5) = 2,
function p(x) = P(X = x) is such that p(1)
p(6) = .3.
(1) Calculate P(X > 4). Calculate P(X = 6|X > 4).
(2) Calculate E(X), Var(X), and SD(X). Plot p(x) in the form of a histogram. Explain
intuitively that E(X) is the center and SD(X) is the spread of the histogram.
(3) Suppose the reward for z is h(x), and h(1) = -$20, h(2) = -$10, h(3) = $0, h(4) = $10,
h(5) $20, h(6) = $100. Calculate E(h(X)), Var(h(X)) and SD(h(X)). What are the units of
=
=
E(h(X)) and Var(h(X))?
(4) Suppose h(x)
E[h(X)] = 2E(X) + 1.
(5) Suppose h(x) = x². Calculate E[h(X)] using the formula E h(r)p(x). Verify that E(X²) >
[E(X)]².
=
2x + 1. Calculate E[h(X)] using the formula E h(x)p(x). Verify that
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