# Question #2006542: Normal Distribution

Question: For independent random variables $$X\sim N\left( -2,7 \right)$$ and $$Y\sim N\left( 3,1.4 \right)$$ :

(a) Compute E(X) and var(X)

(b) In the scratchwork, sketch pdf(X) over the interval [-12, 81] and give coordinates of the peak

(c) For $$Z=4X-5Y$$, compute E(Z) and $${{\sigma }^{2}}=\operatorname{var}\left( Z \right)$$, and determine the distribution of Z

(d) Compute $$\Pr \left( 0\le X\le 3 \right)$$

(e) Compute $$\Pr \left( X\le 1 \right)$$

(f) Find the value of y that satisfies $$\Pr \left( X\le y \right)=0.9$$

Solution: The solution consists of 293 words (4 pages)
Deliverables: Word Document

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