224k views
0 votes
consider the discrete random variable x given in the table below calculate the mean variance and standard deviation of eggs also calculate the expected value of x around solution to three decimal places if necessary

User Carbin
by
7.6k points

1 Answer

2 votes

The mean and the expected value are computed as follows:


\mu=\sum ^{}_{}x_i\cdot P(x_i)

Substituting with data:


\begin{gathered} \mu=1\cdot0.07+6\cdot0.07+11\cdot0.08+15\cdot0.09+18\cdot0.69 \\ \mu=0.07+0.42+0.88+1.35+12.42 \\ \mu=15.14 \\ E(x)=15.14 \end{gathered}

The variance is calculated as follows:


\sigma^2=(x_i-\mu)^2\cdot P(x_i_{})

Substituting with data:


\begin{gathered} \sigma^2=(1-15.14)^2\cdot0.07+(6-15.14)^2\cdot0.07+(11-15.14)^2\cdot0.08+(15-15.14)^2\cdot0.09+(18-15.14)^2\cdot0.69 \\ \sigma^2=(-14.14)^2\cdot0.07+(-9.14)^2\cdot0.07+(-4.14)^2\cdot0.08+(-0.14)^2\cdot0.09+2.86^2\cdot0.69 \\ \sigma^2=199.9396\cdot0.07+83.5396\cdot0.07+17.1396\cdot0.08+0.0196\cdot0.09+8.1796\cdot0.69 \\ \sigma^2=26.860 \end{gathered}

And the standard deviation is the square root of the variance, that is:


\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{26.8604} \\ \sigma=5.183 \end{gathered}

User Bewusstsein
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories