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4.5.1 Statistical distributions (A-level only)

4.5.1 Statistical distributions (A-level only)

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Question 67

The independent random variables XXX and YYY are defined as X∼N(50,42)X \sim N(50, 4^2)X∼N(50,42) and Y∼N(40,52)Y \sim N(40, 5^2)Y∼N(40,52). The random variable AAA is defined as

A=3X−2Y A = 3X - 2Y A=3X−2Y

Find:

a.

E(A)E(A)E(A)

[2]
b.

Var(A)Var(A)Var(A)

[2]
c.

The independent random variables X1,X2,X3,X4,X5X_1, X_2, X_3, X_4, X_5X1​,X2​,X3​,X4​,X5​ each have the same distribution as XXX. The random variable BBB is defined as

B=∑i=15Xi B = \sum_{i=1}^{5} X_i B=i=1∑5​Xi​

Find P(B>4A)P(B > 4A)P(B>4A).

[4]
Markscheme

4.5.1 Statistical distributions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /4.5.1 Statistical distributions (A-level only)

228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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