A nefarious gambler has developed a weighted six-sided die, with sides marked 1,2,3,4,5, and 6. The probability that a 6 is rolled is 0.4, and all the other sides are equally likely. Define the random variable X = the value on the die when it is rolled once. (a) Write out the pmf of X. (b) Compute the probability that an even number is rolled. (c) Compute the expectation and variance of X.

In the geometric progression –3, 12, −48… what term is 3,072?

Select the correct answer from each drop-down menu. a system of equations and its solution are given below. system a complete the sentences to explain what steps were followed to obtain the system of equations below. system b to get system b, the equation in system a was replaced by the sum of that equation and times the equation. the solution to system b the same as the solution to system a.]

Ascientist has 50 grams of a radioactive element. the amount of radioactive element remaining after t days can be determined using the equation (1) after two days the scientist receives a second shipment of 50 grams of the same element. the equation used to represent the amount of shipment 2 remaining after t days is 10) - 50 which of the following is an equivalent form of the expression for the amount remaining in shipment 2? what’s the answer?