81 views

Confidence intervals calculated from other confidence intervals (binomial problem)?

In a binomial experiment, I have an estimate for the probability of 3 independent events A, B & C, each with a 95% confidence interval. (Trivial example values) ...
• 2,119
114 views

What is the conditional $\operatorname{Var}(XY|Y)$ given that $X$ and $Y$ are independent?

What is the conditional $\operatorname{Var}(XY|Y)$ given $X$ and $Y$ are independent? Is it: $$\operatorname{Var}(XY|Y)= Y^2\operatorname{Var}(X|Y) = Y^2\operatorname{Var}(X)?$$
• 33
302 views

Given that X and Y are normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2?

Given that X and Y are independent and normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2?
39 views

exercise autocovariance function

I don't know how to obtain the autocovariance function of the following process, having a multiplication makes it difficult for me. $X_t = Z_t + \theta Z_tZ_{t-1}$ with $Z_i \sim N(0, \sigma^2)$ (...
2k views

Define $Var(XY)$ in terms of $E(X)$, $E(Y)$, $Var(X)$, $Var(Y)$ for Independent Random Variables $X$ and $Y$ [duplicate]

I currently know: $$Var(XY)=E(X^2Y^2)−[E(XY)]^2$$ $$=E(X^2)E(Y^2)−[E(X)]^2[E(Y)]^2$$ but I am lost where to go from there. I can vaguely see the the formula $Var(X)=E(X^2)-E(X)^2$ hidden somewhere, ...
• 31
903 views

Standard deviation/variance for the sum, product and quotient of two Poisson distributions

What would be the standard deviation for $A+B$, $AB$ and $\frac{A}{B}$ for $A$ and $B$ Poisson distributed?
250 views

• 151
197 views

Variance of the difference of products of iid sequences

So suppose you have two sequences $\{Y_t\}$ and $\{Z_t\}$ and they are both iid and independent from each other. Now suppose I have a time series $\{X_t\}$ such that... $$\{X_t\} = Y_t(1-Y_{t-1})Z_t$$...
• 13
117 views

How can I calculate the probability that the product of two independent random variables does not exceed $L$?

I have one variable, $X$, which is provided hourly for a period of one month (720 total values in the series). I have another variable, $Y$, which is provided quarterly (for which I am provided the ...