Practise forming discrete probability functions and cumulative distributions, completing missing table values, and finding probabilities or thresholds from them.
The discrete random variable X has probability function p(x) and cumulative distribution function F(x) given in the table below.
\begin{tabular}{|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 \\
\hline p(x) & 0.10 & a & 0.28 & c & 0.24 \\
\hline F(x) & 0.10 & 0.26 & b & 0.76 & d \\
\hline
\end{tabular}
Two independent observations, and , are taken from the distribution of X.
Write down the value of d
Find the values of a, b and c
Write down the value of P(X>4).
Find the probability that and are both odd.