华赞 · 2022年06月11日
NO.PZ2019040801000013
问题如下：
X's probability is shown as following,
P(X=0.4)=30%, P(X=0.2)= 30%, P(X=-0.2)= 40%.
the standard deviation of X is closest to:
选项：
A.
0.1257.
B.
0.2138.
C.
0.2569.
D.
0.1566.
解释：
C is correct
考点：Expected Value & Variance
解析：先求出X的期望 = 30%*(0.4) + 30%*(0.2) + 40%*(-0.2) = 0.1
那么X的方差就是 30%*(0.4-0.1)2+ 30%*(0.2-0.1)2 + 40%*(-0.2 -0.1)2 = 0.066
Standard deviation = 0.2569
0这个答案怎么算出来的？求步骤
李坏_品职助教 · 2022年06月11日
嗨，努力学习的PZer你好：
先说一下公式：
带有概率的方差计算公式：
σ^2 = P1 * (X1 - μ)^2 + P2 * (X2-μ)^2 + …… + Pn * (Xn - μ)^2， 标准差等于方差开根号。
带有概率的期望（也叫均值）计算公式：
μ = P1 * X1 + P2*X2 + ……+Pn * Xn
根据题干，P1 = 30%, X1 = 0.4。P2= 30%，X2 = 0.2。P3 = 40%, X3 = -0.2.
----------------------------------------------努力的时光都是限量版，加油！
NO.PZ2019040801000013问题如下X's probability is shown following,P(X=0.4)=30%, P(X=0.2)= 30%, P(X=-0.2)= 40%.the stanrviation of X is closest to:A.0.1257.B.0.2138.C.0.2569.0.1566.C is correct考点ExpecteValue Variance解析先求出X的期望 = 30%*(0.4) + 30%*(0.2) + 40%*(-0.2) = 0.1那么X的方差就是 30%*(0.4-0.1)2+ 30%*(0.2-0.1)2 + 40%*(-0.2 -0.1)2 = 0.066Stanrviation = 0.2569E（x）是能求的，E（x平方）是否等于x平方乘以x概率的平方呢？
NO.PZ2019040801000013问题如下X's probability is shown following,P(X=0.4)=30%, P(X=0.2)= 30%, P(X=-0.2)= 40%.the stanrviation of X is closest to:A.0.1257.B.0.2138.C.0.2569.0.1566.C is correct考点ExpecteValue Variance解析先求出X的期望 = 30%*(0.4) + 30%*(0.2) + 40%*(-0.2) = 0.1那么X的方差就是 30%*(0.4-0.1)2+ 30%*(0.2-0.1)2 + 40%*(-0.2 -0.1)2 = 0.066Stanrviation = 0.2569E（x^2）不应该是x^2✖️概率再相加吗
NO.PZ2019040801000013 0.2138. 0.2569. 0.1566. C is corre考点ExpecteValue & Varian解析先求出X的期望 = 30%*(0.4) + 30%*(0.2) + 40%*(-0.2) = 0.1 那么X的方差就是 30%*(0.4-0.1)2+ 30%*(0.2-0.1)2 + 40%*(-0.2 -0.1)2 = 0.066 Stanrviation = 0.2569两个问答看了还是不懂最后一步
NO.PZ2019040801000013 P(0.4)=30%, P(0.2)=30%, P(-0.2) = 40% 在求出来E（x）之后求方差为什么前面的weights: w(0.4)=30%; w(0.2)和w(-0.2)没有平方？只平方了（X- E(x)）?
