Random Variables

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Problems with Discrete Random Variables and Probabilities

Two dice are rolled and the absolute value of the differences between the numbers appearing uppermost are recorded.

a

Complete the sample space.

Die $2$2 | |||||||

1 |
2 |
3 |
4 |
5 |
6 |
||

Die $1$1 | 1 |
$0$0 | $\editable{}$ | $\editable{}$ | $3$3 | $\editable{}$ | $\editable{}$ |

2 |
$1$1 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | |

3 |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $2$2 | $\editable{}$ | |

4 |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | |

5 |
$4$4 | $\editable{}$ | $2$2 | $\editable{}$ | $\editable{}$ | $\editable{}$ | |

6 |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Let $X$`X` be defined as the absolute value of the difference between the two dice. Construct the probability distribution for $X$`X` using the table below.

Enter the values of $x$`x` from left to right in ascending order.

$x$x |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
---|---|---|---|---|---|---|

$P$P$($($X=x$X=x$)$) |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

c

Calculate $P$`P`$($($X<3$`X`<3$)$).

d

Calculate $P$`P`$($($X\le4$`X`≤4$|$|$X\ge2$`X`≥2$)$).

Easy

Approx 8 minutes

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Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal

Apply probability distributions in solving problems