Random Variables

Danielle records her team's winning or losing margins over $10$10 games of the hockey season, with winning margins recorded as positive values and losing margins as negative values. The margins were recorded below.

$X$X |
$-1$−1 | $4$4 | $2$2 | $3$3 | $1$1 | $2$2 | $4$4 | $-1$−1 | $2$2 | $1$1 |
---|

a

Let $X$`X` be the margin of a given game. Summarise this data in a frequency table.

$X$X |
Frequency |
---|---|

$-1$−1 | $\editable{}$ |

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

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

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

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

b

Hence, complete this table for the discrete probability distribution for $X$`X`.

$x$x |
$-1$−1 | $1$1 | $2$2 | $3$3 | $4$4 |
---|---|---|---|---|---|

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

Easy

Approx 3 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