The mean and standard deviation is as follows:

\(E(X+Y)=E(X)+E(Y)\)

\(=80+12\)

\(=92\)

\(V(X+Y)=V(X)+V(Y)\)

\(SD(X+Y)=\sqrt{V(X)+V(Y)}\)

\(=\sqrt{12^{2}+3^{2}}\)

\(=\sqrt{153}\)

\(=12.3693\)

asked 2021-05-18

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: X-20

asked 2021-05-27

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 0.5Y

asked 2021-06-03

X and Y are independent Poisson random variables with means respective \(\lambda_{1} and \lambda_{2}\).

asked 2021-06-06

\(f_{X}(t)=f_{Y}(t)=\begin{cases}\frac{2}{t^{2}},\ t>2\\0,\ otherwise \end{cases}\)

(a)What is the joint probability density function f(x,y)?

(b)Find the probability density of W=XY. Hind: Determine the cdf of Z.

asked 2021-06-07

X and Y are independent normal random variables with respective parameters \((\mu_{1},\sigma_{1}^{2}) and (\mu_{2},\sigma_{2}^{2})\).

asked 2021-05-01

Calculate P(Y|X>2)

asked 2021-01-19

Find the probability that a randomly selected value is between 71.4 and 78.

\(\displaystyle{P}{\left({71.4}{<}{x}{<}{78}\right)}={P}{\left({<}{z}{<}\right)}=\)?

asked 2021-03-09

Find the probability that a randomly selected value is less than 113.4.

\(\displaystyle{P}{\left({X}{<}{113.4}\right)}=\)

Write your answers as numbers accurate to 4 decimal places.

asked 2021-05-23

Find \(P(X+Y>3)\)

asked 2021-06-02

Find \(P(X>Y)\)