Mistakes in problem statement (hierarchical modeling)

[kalish1]

I am doing some problems from a practice final and would like to know if the following problem has mistakes in the way it is written. It is throwing me off.

**Problem statement:** Suppose that $(X_1,P_1), \ldots, (X_n,P_n)$ are independent random vectors with $X_i|P_i \approx Bernoulli(P_i), P_i \approx beta(\alpha_i,\beta_i)$, for $i = 1,2,\dots, n$. Find $P(X_i=k)$.

Shouldn't $P(X_i=k)$ be $P(X_i=n)$, and shouldn't $\approx$ be ~, and shouldn't $(\alpha_i, \beta_i)$ be $(\alpha,\beta)$?

 

[Valkarie]

No, the problem statement is correct as written. $P(X_i=k)$ refers to the probability of the random variable $X_i$ being equal to some value $k$. $\approx$ and ~ are used interchangeably and mean "is distributed as". $(\alpha_i, \beta_i)$ refers to the fact that each $P_i$ has its own parameters; it is not necessary for all of them to have the same parameters.