The weekly demand X for kerosene at a certain supply station has a density function given by [x for 0sxsl S(x) = {1/2 for l

Q: Consider the density function f(x) = k√x, 0<x<1, 0, elsewhere. (a) Evaluate k. (b) Find F(x) and use…

A: Given density function isa) We have to evaluate kb) We have to find F(x) and use it to evaluate

Q: 43. Log-normal distribution. Let X be N (0, 1), and let Y = eX; Y is said to have the log-normal…

A:

Q: The density function of X is given by f(x) = 1- x/2, for 0 < x < 2. Find E(5X?). Find Var(X).

A: Given,f(x)=1-x2     ;  0&lt;x&lt;20             ;  otherwise

Q: The density function of X is given by Sa + br?, 0<I< 1; f(r) = { 0. clsewherce. If o? = var(X) = (a)…

A:

Q: 1. Let f (x) = ln(-x). a. What is its domain? b. Find and simplify its derivative. How does this…

A: Use differentiation

Q: 16. Let a thin rod of length a have density distribution function p(x) = 10e-0.1, where x is…

A:

Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

A:

Q: By choosing small values for h, estimate the instantaneous rate of change of the function f(x) = x³…

A: Use the diffrention formula then simplify

Q: 2. Aprobability mass function is given as f(x) =- for x = 0,1,2,3,. Find P(1.5 < X < 4.2)

A:

Q: With the known values of a = 200,000  and b = 230,000,  the first equation for the probability…

A: Here, a = 200,000 and b= 230,000 f(x) =1/(230000-200000)        =1/30000

Q: |If f(x) = a4 is the parent cubic function, prove that the AVERAGE rate of change of f(x) over the…

A:

Q: L[f(t)] = F(s) = [ e*“ f(t) dt -st

A: The given integral is a Laplace transform, it can be evaluated by the integral by parts method. Let…

Q: [8] 3. In a process of sintering(heating) two types of copper powder, the density function for Y1,…

A:

Q: Find E(X)

A:

Q: Consider a thin wire of mass m and length L going from x = a to x = b. Let the density of the wire…

A: Given that a thin wire of mass m and length L going from x=a to x=b. The density of the wire is…

Q: Consider the case of a continous variable of interest, call it X. Its density function is given by 1…

A: The values which divide a frequency distribution of a variable into hundred equal parts, are said to…

Q: A bacterial culture is growing according to the logistic growth function           y = 1.25 /(1 +…

A: a) The weight of the culture after 0 hours is calculated as follows:…

Q: Let X ~ exp(rate = 3). (a) Find the mgf of X. (b) Use the mgf to find E[X], Var(X), E[X4] and E[X").

A:

Q: (b) For a differentiable function f(x), show that 8(2 = 1) where f' = dj ]dx and a; are the values…

A: We will use the following properties of Dirac delta function to prove the given formula : ∫abδxdx=1…

Q: Let f(x) = e*g(x), where g(0) = 1 and g'(0) = 4. Find f'(0). %3D %3D

A: fx=exgx Differentiating with respect to x, we get f'x=dexdx·gx+dgxdx·ex…

Q: The student should determine the minimum rate of change of the function g(x, y) = y²e*Y on the…

A: First I have written the rule of minimum rate of change of a function at given point and then find…

Q: 2 a- If the continuous RV X has Rayleight density f(x) = a? x U(x), find E(X") and deduce the values…

A:

Q: If f(x) and g(x) represent two curves then Area between x=a and x=b is given by a. Ob. ({x) –…

A:

Q: A card is randomly selected from a deck of 52 playing cards, find the probability that it is I) A…

A: We know that There are 52 cards in the deck divided into two colour i.e red(26) and black (26).…

Q: (4) The mass (in grams) of an insect after t days is given by m(t) = 3+t2, while the volume (in cm³)…

A:

Q: Sketch the level curve of g(x,y) = y / 4 ln x corresponding to g(x,y) = -1/2

A: g(x,y)=y4ln x=-12⇒2y=-4ln x⇒y=-2ln x

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.