COMP 2804 — Assignment 4

•输入您的姓名和学生编号。

1≤i≤6，模具Di的一个面标记为i，而其他五个面标记为零。

X =红色骰子的结果加上蓝色骰子的结果，
Y =红色骰子的结果减去蓝色骰子的结果。
1.证明E（X·Y）= E（X）·E（Y）。
2. X和Y是独立的随机变量吗？与往常一样，请为您的答案辩护。

1/2和一个概率为1/2的女孩，与其他孩子的性别无关。外汇和
XF会在生完一个女孩或四个孩子后立即停止生孩子。

C = FX和XF拥有的子代数，
B = FX和XF拥有的男孩数量。

Hint: If you implement this algorithm and run it several times for large values of n, then you
may recognize the output. For the derivation of your value of E(Y ), use indicator random
variables.
Question 6: In the Lotto 6/49 lottery, you pick a 6-element subset X from the set N =
{1, …, 49} and then a machine picks, uniformly at random, a 6-element subset Y from N.
1. The number |X ∩ Y | of numbers you picked correctly is a random variable. What is
the expected value of this random variable? Give an exact answer, some Python code
2. [Warning: The following is an oversimplification, don’t use it to make life choices.]
The payout in Lotto 6/49 is relative to the Jackpot, which we will call x. The payout
is defined as follows:
• 6 correct numbers: x
• 5 correct numbers x/95
• 4 correct numbers x/4365
• 3 correct numbers 10
• 2 correct numbers 3
If you are given one Lotto 6/49 ticket, what is your expected payout? Give an exact
answer (which will include the variable x).
3. A Lotto 6/49 ticket costs \$3. What is the minimum jackpot value x that gives a payout
of at least \$3?

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