Show that the following function satisfies the properties of a joint probability mass function. xyfxy(x, y) −1.0 −2 1/8 −0.5 −1 1/4 0.5 1 1/2 1.0 2 1/8 determine the following: a. p(x < 0.5, y < 1.5) b. p(x < 0.5) c. p(y < 1.5) d. p(x > 0.25, y < 4.5) e. e(x), e(y), v(x), v(y) f. marginal probability distribution of x

Ben wants to play a carnival game that costs $2. in his pocket he has 5 red tickets worth 35 cents each, and 15 blue tickets worth 10 cents each. which of the following systems of inequalities correctly represents the constraints on the variables in this problem? let represent the red tickets and b represent the blue tickets.

Triangles abc and dfg are given. find the lengths of all other sides of these triangles if: b ∠a≅∠d, ab·dg=ac·df, ac=7 cm, bc=15 cm, fg=20 cm, and df-ab=3 cm.

The water company charges a residential customer $41 for the first 3,000 gallons of water used and $1 for every 200 gallons used over 3000 gallons. if the water bill was $58 how many gallons of water were usedanswersa 3400 gallonsb 6000 gallonsc 6400 gallons d 7000 gallons