[This Version: 09-12-2020]

1.(Stock & Watson 2019, Exercise 2.1) Let Y denote the number of “heads” that occur when two (fair) coins are tossed.

(a)Derive the probability distribution of Y.

(b)Derive the cumulative probability distribution of Y.

(c)Derive the mean and variance of Y.

2.(Stock & Watson 2019, Exercise 2.5) In September, Seattle’s daily high temperature has a mean of 70 degrees Fahrenheit and a standard deviation of 7 degrees Fahrenheit. What are the mean, standard deviation, and variance in degrees Celsius?

3.(Stock & Watson 2019, Exercise 2.9) X and Y are discrete random variables with the following joint distribution:

Y =14 Y =22 Y =30 Y =40 Y =65

X=1 0.02 0 05 0.10 0 03 0.01

X=5 0.17 0 15 0.05 0 02 0.01

X=8 0.02 0 03 0.15 0 10 0.09

This is, Pr(X = 1,Y = 14) = 0.02, and so forth.

(a)Calculate the probability distribution, mean, and variance of Y .

(b)Calculate the probability distribution, mean, and variance of Y given X = 8.

(c)Calculate the covariance and correlation between X and Y .

4.(Stock & Watson 2019, Exercise 2.10) Compute the following probabilities:

(a)If Y is distributed N(1,4), find Pr(Y ≤ 3). (b) If Y is distributed N(3,9), find Pr(Y > 0).

(c)If Y is distributed N(50,25), find Pr(40 ≤ Y ≤ 52).

(d)If Y is distributed N(5,2), find Pr(6 ≤ Y ≤ 8).

Sample Solution

T.S. Eliot's The Love Song of J. Alfred Prufrock TS Eliot's Prufrock T. Early verse "Alfred Prufrock's Love Song" humorous character. Elliott (1888 - 1965) showed up in his title as a sensational speech. Eliot discusses the absence of affection through his speaker This sonnet isn't a "tune", yet contemplation about a sentimental disappointment. The initial picture of the night (customarily the hour of sentiment) is uncomfortable, neither solace nor enticement nor impulse to become "persistent" around evening time (Spender 160): (2-3). T.S. T. S's. clarification of Eliot's "Adoration Song by J. Alfred Prufrock" in Eliot's "Adoration Song by Alfred Prufrock" is tending to the issue of storyteller managing moderately aged issues. Prufrock (storyteller) torments regarding age as a weight. His adoration for a specific lady is on the grounds that he feels that his life is finished. His consideration regarding the progression of time is an attribute of his dread of maturing. - Who is Prufrock? The advanced pattern of unnecessary reflection keeps individuals from carrying on with a satisfying and dynamic life. Is Prufrock valid? See the sonnet guide to help your remark. The appropriate response is clear and self-exorbitant and urgent reflections written in verse by Prufrock "composed by Alfred Prufrock's adoration tune." Eliot] TS Love tune by J. Alfred Prufrock in Eliot's sonnet "J. Alfred Prufrock's affection melody", T. Eliot capably passed on the feelings of different Plufferlocks, and he gave "target relationship" By applying it we made distress for the speaker. It is the official type of a particular feeling ("Hamlet and its issues"). - T. Investigation of Eliot's adoration tune "J. Alfred Prufrock's Love Song" shows the impact of social and financial weight on the lives of Victorian individuals. T. S. Among amusing talks, Elliott gives us that the truth old enough and social position makes us confounded by his feelings of dread. This sonnet starts with "Infernio" of six lines of Dante. This uncommon area clarifies that the speaker is in hellfire and can just pass on data to others in damnation.>

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