已知随机变量X的概率分布为P{X=k}=13，（k=1，2，3），当X=k时随机变量Y在（0，k）上服从均匀分布，即P{Y 已知随机变量X的概率分布为：P{X=K}=P^K,K=1,2...
\u8bbe\u968f\u673a\u53d8\u91cfX\u7684\u5206\u5e03\u4e3aP{X=K}=13\uff0c\uff08K=1\uff0c2\uff0c3\uff09\uff0c\u5f53X=K\u65f6\u968f\u673a\u53d8\u91cfY\u5728\uff080\uff0ck\uff09\u4e0a\u670d\u4ece\u5747\u5300\u5206\u5e03\uff0c\u5219P\uff08Y\u22642.5P\uff08Y\u22642.5\uff09=1-P{Y\uff1e2.5}\u6ce8\u610f\u5230\u4ec5\u5f53X=3\u7684\u65f6\u5019Y\u624d\u6709\u53ef\u80fd\u5927\u4e8e2.5\uff0c\u56e0\u6b64P{Y\uff1e2.5}\uff1dP{X\uff1d3}P{Y\uff1e2.5|X\uff1d3}\uff1d133?2.53\uff1d118\u2234P{Y\u22642.5}\uff1d1?118\uff1d1718\u6545\u7b54\u6848\u586b1718
\u5148\u8ba1\u7b97\u7ea7\u6570
p^1+p^2....+p^k... = p/(1-p)
\u5c31\u662f\u8bf4P(N*)=p/(1-p)=1 \u89e3\u5f97p=1/2
| 3 |
| k＝1 |
P{X＝k}＝
| 1 |
| 3 |
根据全概率公式得：
P{Y≤2.5}＝
| 3 |
| k＝1 |
=
| 3 |
| k＝1 |
=
| 1 |
| 3 |
| 2.5 |
| 3 |
=
| 1 |
| 3 |
| 17 |
| 3 |
=
| 17 |
| 18 |
故答案为：
| 17 |
| 18 |
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