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Choose between scaling one value and adding independent values

X and Y are independent continuous normal random variables with means 10,12 and standard deviations 2,3 respectively. Find

(a) P(Y<10)P(Y<10),

(b) P(2X>25)P(2X>25),

(c) P(Y<X)P(Y<X),

(d) P(4X+5Y>90)P(4X+5Y>90),

(e) x such that P(X1+X2>x)=0.25P(X_1+X_2>x)=0.25, for independent observations X1,X2X_1,X_2 of X.

[1987/II/9]

CJC · Discussion · Question 7

A factor multiplies one variable’s variance by its square; independent copies contribute separate variances.

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