Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x −41 −27 −8 −3 P(X = x) 0.29 0.35 0.21 0.15

a) Mean is -23.47

b) Variance is 206.59

c) standard deviation is 14.37

Step-by-step explanation:

Given that;

 x              −41        −27        −8         −3

P(X = x)      0.29      0.35      0.21      0.15

X.P            -11.89     -9.45    -1.68     -0.45

a) mean

Mean = ∑X.P = -11.89 +  -9.45 + -1.68 + -0.45

Mean = -23.47

b)  the variance

E(x²) = ∑x²P(X=x)

= (−41²×0.29) + (−27²×0.35) + (−8²×0.21) + (−3²×0.15)

= 487.49 + 255.15 + 13.44 + 1.35

= 757.43

So

Var(X) = E(x²) - [∑X.P]²

Var(X) = 757.43 - [-23.47]²

= 757.43 - 550.8409

= 206.5891 ≈ 206.59

Therefore Variance is 206.59

c) standard deviation

standard deviation SD(X) = √Var(X)

SD(X) = √206.5891

= 14.3732 ≈ 14.37

Therefore standard deviation is 14.37

a² + b²= c²

24² + 7² = c²

c= 25

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.