The random variable x takes on the values 1, 2, or 3 with probabilities (1 + 3k)/3, (1 + 2k)/3, and (0.5 +5k)/3, respectively.(a) Find the appropriate value of k.(b) Find the mean and variance of x.(c) Find the cumulative distribution function.

a)

We can multiply both sides by 3 and we got:

And if we replace we got:

X            1             2               3

P(X)    0.383      0.367        0.25

b)

c) X            1                         2                              3

F(X)       0.383      0.367+0.383=0.75        0.25+0.75 = 1

Step-by-step explanation:

For this case we have the following probability mass function given:

X            1             2               3

P(X)  (1+3k)/3    (1+2k)/3   (0.5+5k)/3

Part a

In order to satisfy the definition of probability distribution the sum of all the probabilities needs to be 1 and each of the individual probabilities needs to be higher or equal than 0, using this we can do that:

We can multiply both sides by 3 and we got:

And if we replace we got:

X            1             2               3

P(X)    0.383      0.367        0.25

And we satisfy all the conditions.

Part b

For this case we can find the mean using this formula:

For the variance we need to find the second moment first like this:

And we can find the variance with this formula:

Part c

The cumulative distribution on this case is given by:

X            1                         2                              3

F(X)    0.383      0.367+0.383=0.75        0.25+0.75 = 1

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.

step-by-step explanation: