The following is the probability mass function for the number of times a certain computer program will malfunction: 0 1 2 3 4 5 p(x) | 0.05 0.28 0.42 0.15 0.08 0.02 (a) what is the probability that the computer program will malfunction more than 3 times? (b) compute e(x), e(x2), and v(x). e(x) = e(x2) = v(x) = (c) suppose y, the time in minutes to fix malfunctions, relates to the number of times the program malfunctions, by the function: y = 9*x . what is the expected time in minutes needed to fix malfunctions in the program? d) what is the variance of the time in minutes to fix the malfunctions?

a)P(X>3)=0.1

b)

E(X)=1.99

E(X²)=5.09

V(X)=1.13

c) E(Y)=17.91

d) V(Y)=81*V(X)=91.5

Step-by-step explanation:

a)

P(X>3)=P(X=4)+P(X=5)=0.08+0.02=0.1

b)

E(X)=∑x*p(x)=0*0.05+1*0.28+2*0.42+3*0.15+4*0.08+5*0.02=1.99

E(X²)=∑x²*p(x)=0*0.05+1*0.28+4*0.42+9*0.15+16*0.08+25*0.02=5.09

V(X)=E(X²)-(E(X))²=5.09-3.96=1.13

c)

E(Y)=9*E(X)=9*1.99=17.91

d)

V(Y)=9²*V(X)=81*V(X)=81*1.13=91.5

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: