Dennis is testing model airplanes. He starts with n model planes which each independently have probability p of flying successfully each time they are flown, where 0 (a) What is the distribution of X? That is, what is PX,-
(b) What is the distribution of Xs? That is, what is PK2 Show that X2 follows a binomial distribution by finding some n' and p' such that X2Binom(n',p')
(c) Repeat the previous part for X, for arbitrary t 21.
(d) What is the probability that at least one model plane still remains (has not crashed yet) after t days? Do not have any summations in your answer.
(e) Considering only the first day of flights, is the event A1 that the first and second model planes crash independent from the event B1 that the second and third model planes crash? Recall that two events A and B are independent if PAnB PAPB. Prove your answer using this definition
(f) Considering only the first day of flights, let A2 be the event that the first model plane crashes and exactly two model planes crash in total. Let B2 be the event that the second plane crashes on the first day. What must n be equal to in terms of p such that A2 is independent from B2? Prove your answer using the definition of independence stated in the previous part
(g) Are the random variables X, and Xj, where i < j, independent? Recall that two random vari ables X and Y are independent if PX = ki n Y = k2] = PlX = kJEY Prove your answer using this definition k2] for all ki and k2.

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.

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116