Math Answers

Find the general solution of the equation:

𝑥^2𝑦" − 9𝑥𝑦′ + 25𝑦 = 0

Solve the initial value problem:

𝑥^2𝑦" + 𝑥𝑦′ + 9𝑦 = 0; 𝑦(1) = 2, 𝑦′(1) = 0

Find the general solution of the equation:

𝑥^2𝑦" − 7𝑥𝑦′ + 12𝑦 = 0

Given population of 5000 scores with mean=86 and standard devation=10. How many scores are between 76 and 86

a population consist of the values(1,4,3,2) consider samples of size 2 that can be drawn from this population

The top-selling Amar tire is rated 70,000 KMs, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of 82,000 KMs and a standard deviation of 6,400 KMs. What is the probability that a tire wears out before 70,000 KMs? What is the probability that a tire lasts more than 100,000 KMs? Note: You may use Z-table for this

A10. If X and Y are independent binomial random variables with identical parameters n

and p, show analytically that the conditional probability of X, given that X + Y = m

is the hypergeometric distribution.

Determine whether the functions ƒ(𝑥) = √4−𝑥2 is continuous on the interval

 [−4,4]. Show your complete solution.

Determine whether the following functions are continuous at a given point. Show your complete solution.

1. ƒ(𝑥) = 𝑥2−4 at 𝑥 = 2 𝑥−2

2. ƒ(𝑥) = 𝑥2−25 at 𝑥 = 2 𝑥−5

Suppose that a random variable X has a Poisson distribution with parameter λ. The

parameter λ itself is a random variable with the exponential distribution with mean 1

c ,

where c is a constant. Show that

P(X = k) =

c

(c + 1)k+1