Show that the result given in exercise 3.158 also holds for continuous random variables. that is, show that, if y is a random variable with moment-generating function m(t) and u is given by u = ay + b, the moment-generating function of u is etbm(at). if y has mean μ and variance σ2, use the moment-generating function of u to derive the mean and variance of u.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: