Stats_mix_problems ch1-6

• args = $\mu ,\sigma$? → some norm,
• = $n,p$? some binom

Find $P(X>15)$ where $X\sim \text{Bin}(n=20,p=0.6)$

> 1 - pbinom(15,20,0.6) 
> [1] 0.05095195

$P(Y<14)$ where $Y\sim \text{N}(\text{mu}=20,\text{sigma}=10)$

> pnorm(14,20,10) 
> [1] 0.2742531

If $L=2Y_1+2Y_2-3Y_3$ and $Y_i\stackrel{iid}{\sim }N(mu=3,{\sigma }^2=2)$ find $V(L)$

> V(L) (4 + 4 + 9)*2 
> [1] 34

Suppose Y~Gamma($\alpha =2,\beta =3$) Then P(Y < -7) = 0 ?

True

Measuring btwn 2-3, so impossible to fall in -7