Please write a summary on quadratic expressions of normally distributed random variables and their distribu- tion. Present the results in matrix/vector form. In you answer, include a quadratic expression that involves the distribution of where X and Ỹ are the sample means of a random sample (X1, Y1),..., (X,n, Yn) from a bivariate normal distribution.

Q: Find the percentile for the data point. Data set: 51 33 41 72 74 75 32; data point 51

A: 51 33 41 72 74 75 32  

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A: Here use basic probability rule Here total 6 kids  And they are line up for recess

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A: Given,n=75x=29sample proportion(p^)=xnp^=2975≅0.38671-p^=1-0.3867=0.6133α=1-0.99=0.01α2=0.005Z0.005=...

Q: In the game of roulette, a player can place a $6 bet on the number 3 and have a a probability of win...

A: Expected value: E(x) = 210(1/38) + (-6)37/38= (210-222)/38 = -12/38 = -$0.3158  

Q: 3, 5, 5, 4, 2, 2, 1, 1, 1, 4, 5, 3, 3 calculate variance

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A: Please see the handwritten solution

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A: * ANSWER :-   

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A: Given that  The data are -1,0,3,5 Find the value (∑X)2

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Q: Jennifer is a financial consultant.                 She tells her client that the probability of mak...

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A: Givensample size(n)=12p=0.50Let "x" be the jury would have femalesx~Binomial(n=12,p=0.50)P(X=x)=(nx)...

Q: let z be the standard normal random variable. 2 Find  P(z < 1.24)       a 0.9371   b 0.8925   c 0.8...

A: Given that  Z be the standard normal random variable  Find P(z&lt;1.24)=

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Q: 42. What is the value of EX? - 5 for the scores: -3, 0, 3, 6?

A: