Question

The random variables X and Y represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period in the day. The joint distribution is $$f(x,y)=\left(\frac{1}{4^{x+y}}\right)\left(\frac{9}{16}\right)$$ for $$x=0, 1, 2, 3,...$$ and $$y=0, 1, 2, 3,...$$ Consider $$Z=X+Y$$, the sum of the two, Find $$E(Z)$$ and $$Var(Z)$$

Name: the random variables x and y represent the number of vehicles that arrive at two separate street corners during a certain 2 minute period in the day the joint distribution is fxyleftfrac14xy 10243
Uploaded: 2021-06-16T13:45:04-08:00
Duration: 3 min 34 s
Channel: Christopher Stanley
Description: the random variables x and y represent the number of vehicles that arrive at two separate street corners during a certain 2 minute period in the day the joint distribution is fxyleftfrac14xy 10243

          The random variables X and Y represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period in the day. The joint distribution is
$$f(x,y)=\left(\frac{1}{4^{x+y}}\right)\left(\frac{9}{16}\right)$$
for $$x=0, 1, 2, 3,...$$ and $$y=0, 1, 2, 3,...$$
Consider $$Z=X+Y$$, the sum of the two, Find $$E(Z)$$ and $$Var(Z)$$

$the random variables x and y represent the number of vehicles that arrive at two separate street corners during a certain 2 minute period in the day the joint distribution is fxyleftfrac14xy 10243$

Added by James L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Christopher Stanley

06/16/2021

Step 1

..$$ and $$y=0, 1, 2, 3,...$$ We can rewrite the PMF as: $$f(x,y) = \frac{9}{16} \left(\frac{1}{4}\right)^{x+y} = \frac{9}{16} \left(\frac{1}{4}\right)^x \left(\frac{1}{4}\right)^y$$ To find $$E(Z)$$ and $$Var(Z)$$, where $$Z = X+Y$$, we first need to find the Show more…

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The random variables X and Y represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period in the day. The joint distribution is $$f(x,y)=\left(\frac{1}{4^{x+y}}\right)\left(\frac{9}{16}\right)$$ for $$x=0, 1, 2, 3,...$$ and $$y=0, 1, 2, 3,...$$ Consider $$Z=X+Y$$, the sum of the two, Find $$E(Z)$$ and $$Var(Z)$$