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Now suppose that I transform this random variable in some way. For instance, suppose that I square it. Now I have a new random variable,

We know the probability distribution of

But we know the probability that

Possible value of X, called x |
Possible value of Y, called y |
P(X=x) which is P(Y=y) also |

0 | 0 | (0.4)^{3} |

1 | 1 | 3(0.6)(0.4)^{2} |

2 | 4 | 3(0.6)^{2} (0.4) |

3 | 9 | (0.6)^{3} |

On to the sample mean as a random variable.

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