Recent content by lerem456

Thank you Jameson and chisigma for your help. The material makes more sense now.

I think I understand now. I've noticed inconsistencies in my work in regard to $\bar{X}$. $\bar{X}\sim N(2, \frac{2}{35})$ from part (a) $\bar{Y}\sim N(1, \frac{2}{15})$ from part (c) $\bar{X} + \bar{Y} \sim N(2 + 2, \frac{2}{35} + \frac{2}{15}) = \sim N(4, \frac{4}{21})$

For part (d) I made an addition error. $\bar{X} \sim N(70, 2)$ $\bar{Y} \sim N(15, 2)$ $\bar{X} + \bar{Y} = \sim N(70+15, 2+2) = \sim N(90, 4)$

Thanks, that makes sense. Part (b) deals with finding the probability of $\bar{X}$ and part (d) is addition with normal variables. I thought it would be easier to work with two normal distributions but if it's unnecessary then I will look to change my work.

I can't approximate using a normal distribution?

Thanks chisigma. So the total distribution would be $\bar{X} \sim N(\lambda=\sum_iX_i, \lambda=\sum_iX_i) = N(70, 70)$ where as each individual distribution would be $\bar{X_i} \sim N(\lambda_i, \frac{\lambda_i}{n})=N(2, \frac{2}{35})$

Let $X_1, ..., X_{35}$ be independent Poisson random variables having mean and variance 2. Let $Y_1, ..., Y_{15}$ be independent Normal random variables having mean 1 and variance 2. (a.) Specify the (approximate) distributions of $\bar{X}$. (b.) Find the probability $P(1.8 \leq \bar{X}...