X is a continuous random variable having p.d.f. f(x) such that f(x) = kr Osxs5 otherwise Find : (a) the constant k; (b) P(1SXS 2); (c) (d (e) Var (X); E(X); E(3X + 1); E(X?); () (g) Var (4X - 5);

Q: Suppose that Var(X) = 742.23, Var(Y) = 8890.5, and Cov(X,Y) = 2191.72. What is Var(.51X + .49Y)?

A: The objective of the question is to find the variance of the linear combination of two random…

Q: Suppose Var(X) = 96, and a = .45. What is Var(aX)?

A: The objective of this question is to find the variance of the random variable aX, given the variance…

Q: Let f(x) =x²-x -5 and gx)= -8x+4. Find g(3) and f(g(3)). %3D 9(3) = f(g(3)) = %3D %3D

A:

Q: Let x be the number of teachers among 3 people selected randomly from a group  consisting of 3…

A: Probability: Probability is the ratio of favourable outcomes to all other potential outcomes of an…

Q: Suppose we have the quadratic function f(x)=A(x^2)+2X+C where the random variables A and C have…

A: Let the quadratic equation is f(x)=Ax2+2X+C. From the question, f(A)=A2     0≤A≤2 f(C)=3C2    0≤C≤1…

Q: Differentiate. f(x) = (x 2 - 2x + 4)ex O ex(x² + 2) O ex(x² + 4x + 2) 3 +x+4 O ex(2x - 2)

A: Given the function fx=x2-2x+4ex

Q: a) f(x) = {(3, –4), (2, 1), (–9,–3)} |

A: We have to find domain and range

Q: Let X and Y be jointly cantinuous random variables with joint PDF is given: $ X,Y (x.y) = (1+x*y)…

A:

Q: Let X a b(4,) find Var(3x) and distribution function.

A:

Q: b) Find the variance Var(X) of X.

A:

Q: Suppose that the random change in value of a financial asset is X over the first day and Y over the…

A: The variance of X+Y is calculated asVarX+Y=VarX+VarY-2CovX,Y

Q: evaluate L-1 { t/(s-2)(s+3)}

A: By using partial fraction and table of Laplace transform we solve the given problem as follows :

Q: If X~ GAM(1,2) then Var(X)= 4 (1

A: We have to solve given problem:

Q: find the probability that the number of the red candy is between(E(X)-1) and (E(X)+1)

A: Consider the probability distribution table, X 0 1 2 3 4 5 f 21 29 27 26 18 30 P(X) 21151…

Q: (6) (x)어

A: we have been given f4(x)=(x2+1)2 we have to find the value of f6(x).

Q: If 25% of the oranges produced by a farm is defective in a random sample of 20 oranges, then if the…

A: Given 25% of total 20 oranges are defective, To calculate (X>3) if X represents the number of…

Q: Express var(X + Y), var(X − Y), and cov(X + Y, X −Y) in terms of the variances and covariance of…

A: From the property of Variance we know that Var(ax+by)= a2 +b2 +2abcov(x,y) ...(1) Substitute…

Q: Differentiate. f(x) = In (4x + 1)(x+7)³ (1 - 6x)5

A: The solution is given below:

Q: x(k)-3x(k-1) + 2x(k-2)= e(k), e(k)= [1, k = 0, 1 0, k ≥2 x(-2) = x(-1)=0

A:

Q: Evaluate S 2x + 1 (4x + 3)(x + 1) - dx

A: Consider the integral

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A:

Q: Show that variance o? (x²) – ((x))²

A: Solution

Q: Use the rules of expectations to show that Var(X) = E(X-E(X))") E(X)- E(X) and Var(X +Y) = Var(X) +…

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!