We can write out mean as an expected value: μ=E[X]
And likewise for variance: σ2= Var(X)
n: number of trials x: number of success in n trials p: probability of success in each trial
Properties of Expectation:
⋅E[X+a]=E[X]+a ⋅E[bX]=bE[X] ⋅E[X+Y]=E[X]+E[Y]
Or in full generality: ⋅E[X1+X2+⋯+Xn]=E[X1]+E[X2]+⋯+E[Xn]
Properties of Variance: ⋅ Var[X+a]= Var[X] ⋅ Var[bX]=b2Var[X] ⋅ Var[X+Y]= Var[X]+ Var[Y] if X and Y are independent
A certain car breaks down every 50 hours of driving time. If the car is driven for a total of 175 hours;
Clara is trying to make the perfect teapot out of pottery. Each time she attempts to make the perfect teapot she will use a lump of clay and she will succeed with a probability of 0.20. Once she makes the perfect teapot she will stop potting.
Suppose we have two independent random variable one with parameters E[X]=4 and Var(X)=3, and the other with parameters E[Y]=9 and Var(Y)=6.
Properties of expectation
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