For the following probability mass function, p(x)=1/x for x=2, 4, 8 p(x) = k/x2 for x=16...

For the following probability mass function, p(x)=1/x for x=2, 4, 8 p(x) = k/x2 for x=16 Find the value of k. Find the standard deviation of (7-9X).

Expert Solution

1) for this to be valid:

P(x) must be equal to 1

therefore P(x) =P(2)+P(4)+P(8)+P(16)=(1/2)+(1/4)+(1/8)+k/256 =1

k/256 =1/8

k=32

2)

x	P(x)	xP(x)	x²P(x)
2	1/2	1.0000	2.0000
4	1/4	1.0000	4.0000
8	1/8	1.0000	8.0000
16	1/8	2.0000	32.0000
	total	5.0000	46.0000

	E(x) =μ=	ΣxP(x) =	5.0000
	E(x²) =	Σx²P(x) =	46.0000
	Var(x)=σ² =	E(x²)-(E(x))²=	21.0000
	std deviation=	σ= √σ² =	4.5826

hence standard deviation of 7-9X =9*SD(X) =9*4.5826 =41.2432

orchestra answered 2 years ago

1. The probability mass function of a discrete random variable X is defined as p(x) =...

1. The probability mass function of a discrete random variable X is defined as p(x) = ax for x = 1, 2, 4, 8 (p(x) =0 for all other values) then the value of a is? 2. Let X be a discrete random variable with Var(X) =6.0 and E(X2) = 17.00. Then: E(X) = ? 3. If X is a binomial random variable with parameters n and p, i.e. X ~ b(x; n, p), then the expected value of X...

A discrete random variable named X has the following pmf (probability mass function): X P(x) 1...

A discrete random variable named X has the following pmf (probability mass function): X P(x) 1 0.6 3 0.2 7 0.1 11 0.1 17a) Find P(X>6) 17b) What is the probability two independent observations of X will both equal 1? 17c) Find the population mean also known as E(X)= the expected value of 17d) Find the population variance of X with both the “regular” formula and “convenient” formula Make a table and show your work. You should get the same...

1. For the following function ?(?) = (?^2−8?+16) / (?^2−4) a. Find the critical values b....

1. For the following function ?(?) = (?^2−8?+16) / (?^2−4) a. Find the critical values b. Use the FIRST DERIVATIVE TEST to determine the intervals where the function is INCREASING and DECREASING. c. Find the RELATIVE EXTREMA of the function and state where they occur. d. Find the ABSOLUTE EXTREMA of the function on the interval [−1, 1.75]

1. For the function P(x) = 4x^2 - 16 / x^2 -5x find the a) List X...

1. For the function P(x) = 4x^2 - 16 / x^2 -5x find the a) List X Intercept(s) if any b) List Y Intercept(s) if any c) List Horizontal Asymptote(s) if any d) List Vertical Asymptote(s) if any e) Domain 2. precalculus

A ﬁrm has the following long run production function x = a(K^1/2)(L^1/2)(P^1/4), where a > 0...

A ﬁrm has the following long run production function x = a(K^1/2)(L^1/2)(P^1/4), where a > 0 is a constant and K, L , P are inputs of the three factors. The prices of K, L , P are Rs. 1 , Rs. 9 and Rs. 8 respectively. a) Derive the ﬁrm’s long run total cost function , long run average cost function and long run marginal cost function. Show the workings in detail b) In the short run P is...

q = K^1/2 L^1/2 p=$20, v=$8, w=$4 a) suppose k= 16, find short-run total and marginal...

q = K^1/2 L^1/2 p=$20, v=$8, w=$4 a) suppose k= 16, find short-run total and marginal costs, and also firm supply function. Find the price that the firm shuts down its production. b) find firm profit maximization demand function and short-run supply function

Consider a discrete random variable with the following probability mass function x 0 1 2 3...

Consider a discrete random variable with the following probability mass function x 0 1 2 3 4 5 p(x) 0.1 0.1 0.2 0.3 0.2 0.1 Generate a random sample of size n =10000 from this distribution. Construct a bar diagram of the observed frequencies versus the expected frequencies.(using R)

Suppose the probability mass function of a random variable X is given by ??x−1?pr(1−p)x−r, ifx=r,r+1,r+2,... f(x)...

Suppose the probability mass function of a random variable X is given by ??x−1?pr(1−p)x−r, ifx=r,r+1,r+2,... f(x) = r−1 0, otherwise If this is the case then we say X is distributed as a Negative Binomial Random Variable with parameters r and p and we write X ∼ NegBin(r, p) (a) If we set r = 1, what distribution do we get? (b) Explain what this random variable models and justify the formula. (Hint: See Section 4.8.2 in Ross.) Math 241...

Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf)...

Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf) of a random variable X, where b is constant. A. Find the value of b B. Find the mean μ C. Find the variance σ^2

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 &nbsp

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 = 0 otherwise find its expectation and variance. b. The two regression lines are 2X - 3Y + 6 = 0 and 4Y – 5X- 8 =0 , compute mean of X and mean of Y. Find correlation coefficient r , estimate y for x =3 and x for y = 3.

Question