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Scale one observation or combine independent variables

Independent random variables satisfy X∼N(100,49)X\sim N(100,49) and Y∼N(110,576)Y\sim N(110,576). Find (i) P(3X<250)P(3X<250), (ii) P(X+Y>200)P(X+Y>200), (iii) P(Y>X)P(Y>X), (iv) P(2X+Y<300)P(2X+Y<300).

CJC · Lecture · Example 7

The source gives both the transformed-distribution and original-event methods for (i).

For independent variables, coefficients enter means linearly and variances as squares.

Read the worked solution