E(0.5Y)=0.5E(Y)

\(=0.5\times 12\)

=6

\(V(0.5Y)=0.5^{2}V(Y)\)

\(=0.5^{2}V(Y)\)

\(SD(0.5Y)=0.5\times SD(Y)\)

\(=0.5\times 3\)

=1.5

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 2021-06-01

asked 2021-06-04

Let \(X_{1}, X_{2},...,X_{n}\) be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables.

Find n such that \(Pr(X>2000)\geq 0.95\).

Find n such that \(Pr(X>2000)\geq 0.95\).

asked 2021-05-26

Random variables \(X_{1},X_{2},...,X_{n}\) are independent and identically distributed. 0 is a parameter of their distribution.

If \(X_{1}, X_{2},...,X_{n}\) are Normally distributed with unknown mean 0 and standard deviation 1, then \(\overline{X} \sim N(\frac{0,1}{n})\). Use this result to obtain a pivotal function of X and 0.

If \(X_{1}, X_{2},...,X_{n}\) are Normally distributed with unknown mean 0 and standard deviation 1, then \(\overline{X} \sim N(\frac{0,1}{n})\). Use this result to obtain a pivotal function of X and 0.

asked 2020-12-07

\(\displaystyle\frac{{{\left(\overline{{{x}_{{1}}}}-\overline{{{x}_{{2}}}}\right)}-{\left(\mu_{{1}}-\mu_{{2}}\right)}}}{{\sqrt{{\frac{{{\sigma_{{1}}^{{2}}}}}{{{n}_{{1}}}}+\frac{{{\sigma_{{2}}^{{2}}}}}{{{n}_{{2}}}}}}}}\)

Give the name of the distribution and any parameters needed to describe it.

asked 2021-09-03

Let \(\displaystyle{X}_{{1}},{X}_{{2}},\dot{{s}},{X}_{{n}}\) be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables. Find n such that Pr\(\displaystyle{\left({X}{>}{2000}\right)}\geq{0.95}\)

asked 2020-10-28

Find the probability that a randomly selected value is between 151.4 and 283.7.

\(\displaystyle{P}{\left({151.4}{<}{X}{<}{283.7}\right)}=\) Incorrect

Write your answers as numbers accurate to 4 decimal places.