Edexcel A-Level Mathematics AS S1.5.2 Probability and Cumulative Distribution Functions Questions

Practise reading and forming p(x) and F(x), then using them to find probabilities, missing constants and threshold values.

Exam points

use p(x)=P(X=x) to find missing probabilities or complete a distribution table

[Maximum number: 7]

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, $X_1$ and $X_2$ , are taken from the distribution of X.

Figure for Question Edexcel A-Level Mathematics AS S1.5.2 Probability and Cumulative Distribution Functions Questions question 1 — Edexcel A-Level Mathematics AS

(a)

Write down the value of d

[ 1 ]

(b)

Find the values of a, b and c

[ 3 ]

(c)

Write down the value of P(X>4).

[ 1 ]

(d)

Find the probability that $X_1$ and $X_2$ are both odd.

[ 2 ]

$P(X\text{ is odd})=0.10+0.28+0.24=0.62$ $P(X_1\text{ and }X_2\text{ are both odd})=0.62^2=0.3844$
awrt 0.384

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Edexcel A-Level Mathematics AS S1.5.2 Probability and Cumulative Distribution Functions Questions question 1

Question (a)

Question (b)

Question (c)

Question (d)