The random variable X has the binomial distribution with probability mass function 6-х 6! p(x) = ,x = 0,1,2,3, ... ,6 х! (6 — х)! a) Derive E(X) and Var(X) b) Find P(X < 1) exactly.

Q: Q2/(a) Let X be a random variable with p.d.f. 1<x<o S(x) = { find k. o.w (b) Let X be a random…

A: For the p.d.f to be valid, ∫1∞kx-2dx=1⇒k∫1∞x-2dx=1⇒k-1x1∞=1⇒k-1∞+11=1⇒k(0+1)=1⇒k=1

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A:

Q: A discrete random variables X has the following probability distribution 1 3-x| P(X = x) for…

A: The probability distribution is PX=x=1Q-3-x16

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A: Introduction- Moment of a random variable - The moments of a random variable or of its distribution…

Q: If a procedure meets all of the conditions of a binomial distribution except the number of trials is…

A: See the hand written solution

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A: X=3 X=4 X=5 X=6 Total Y=4 7114 8114 9114 10114 34114 Y=5 8114 9114 10114 11114 38114…

Q: If x is a random variable (3,x-bn), find the smallest value for n so that it achieves 0.8 <(1 2 p(x)…

A: If a random variable X follows binomial distribution. X~Bx, n, p=13 and PX≥1&gt;0.8 We need to find…

Q: Consider a random variable K with parameter p, whose probability mass function (PMF) is given by…

A: Solution: From the given information, the probability mass function is

Q: For a uniform random variable U∼U(0,14)U∼U(0,14), find the probability P(U>11)P(U>11): P(U>11)

A: From the provided information, U~U(0, 14) a = 0 and b = 14

Q: If ‘X’ is a continuous random variable, then the expected value is given by ?

A: For a continuous random variable X it can take values over a continuous range. So while computing…

Q: The probability distribution of random variable X is a) b) c) d) Show that k = 6. Find P(X <3). P(X=…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: Q4\Let a discrete random variable X has values 1, 2, and 3, with probabilities respectively. a) What…

A: Given: Random variable x which having the values 1, 2 and 3 and its corresponding probability is…

Q: d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X =…

A: Given problem Given that   d)   The random variable X has a Poisson distribution such that P( X=0…

Q: (40) Let X be a random variable with p.d.f. (k +4)e¯3x f(x) ={ 01) O.w

A: a)Use the condition of valid pdf to find the value of k…

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A: Solution

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A:

Q: Rolling a fair n-sided die gives us a random number uniformly distributed among {1, 2,..., n} (our…

A: (a) Since the die is fair, each of the numbers 1,2,…,n has an equal probability of 1n of appearing…

Q: (5) Let X be a random variable with p.d.f. k 1<x<o 2 f(x) =< , find k. O.w

A: Given: fx=kx2            1&lt;x&lt;∞0                 Otherwise

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A:

Q: 1) Let the probability function of a discrete random variable X be 100) = {(²+²) (0.5) (05) 1-²,…

A: Solution

Q: Q2/(a) Let X be a random variable with p.d.f. kx 1<x<∞ S(x)=• find k. O.w

A: The p.d.f of X is given below: fx=kx-2   1&lt;x&lt;∞0          ow

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A: Given information: Let X be a random variable that denotes the number of decays. The sample size is…

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A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2) Required probability is given by 99 P(X 2 100) = 1 - (C")-0.01°- 0.99-3 = 1 - 0.0092427 0.990757…

A: Here the given probability calculation is given :

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Q: (a) The friendly instructor went to visit the casino to play with a biased coin, where the head…

A: Solution: From the given information, the probability of head is p=1/5=0.2.

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A: A circular coin of diameter a is thrown onto a square grid whose squares are b x b. Where, (a &lt;…

Q: (40) Let X be a random variable with p.d.f. (k +4)e-3* f(x) =- 01) O.w

A:

Q: what's r and e, both greater than 0 so that  P(4 < T < 16) =P(r< Z < e)

A: Given that Z~ N( mean=5, SD=3) then  P=(Z-mean)/SD= (Z-5)/3 follows standard normal distribution i.e…

Q: (1) Let X be a random variable with p.d.f. e 0<x<0 k ƒ(x) = < find k. O.W

A: Let X be a random variable with pdf  fx=1ke-8x        0&lt;x&lt;∞0                         otherwise…

Q: Q4\Let a discrete random variable X has values 1, 2, and 3, with probabilities respectively. a) What…

A: The probability distribution table is given by: x 1 2 3 P(X) 12 14 14

Q: (i) Determine the value ofk (ii) Let a = -1 and b = 2.

A:

Q: Both K and M has standard normal distribution and they are independent random variables. Z=K+M Find…

A: Given that, K and M has independent normal distribution and they are independent random variables. Z…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.