Math Answers

true/false? justify.If X has the distribution N(10, 9) and if Y = 5X − 3, then Y has distribution
N(53, 84).

A manufacturer of automobile seats has a production line that produces an average of
100 seats per day. Because of new government regulations, a new safety device has
been installed, which the manufacturer believes will reduce average daily output. A
random sample of 15 days output after the installation of the safety device is shown:
93, 103, 95, 101, 91, 105, 96, 94, 101, 88, 98, 94, 101, 92, 95 .
Assuming that the daily output is normally distributed, is there sufficient evidence to
conclude that average daily output has decreased following the installation of the
safety device? (Use α = 0.05 )

Determine the value of c so that the following functions represent the joint pmf of
the random variables X and Y .
i) f (x, y) = c(x + y +1), x = 0, 1, 2, 3 and y = 0, 1, 2 .
ii) f (x, y) = c(x^2 + y^2), x = −1, 1 and y = −2, 2

Let A and B be two events associated with an experiment such that 4 P(A) = 0. and
P(A ∪ B) = 0.7 . Compute ) P when (B
i) A and B are mutually exclusive.
ii) A and B are independent.

The amount of apples (in kg) produced per day by 10 orchards are given below:
218.2 179.5 207.3 224.3 213.7
199.7 184.7 194.4 203.5 185.4
Find the first four moments about the mean and the coefficient of kurtosis for the
above data.

IN ANY TRIANGLE ABC, IF SIN^2A = SIN^2B + SIN^2C ; PROVE THAT THE TRIANGLE IS RIGHT ANGLED AT A

3 batteries are chosen at random from 15 batteries from which 5 are defective. Find the probability that:

A) none of the three are defective
B) exaxtly one is defective
C) 2 defective and one nondefective
D)at least one is nondefective.

Please type the solution. Im struggling~~ :( Please help meeeee~ THANK YOUUU~

1. Projectile Range
The range r of a projectile fired with an initial velocity at an angle with the horizontal is R= (initial velocity)^2Sin2(angle)/g where g is the acceleration due to gravity. Find the angle such that the range is maximum.

2. Illumination
A light source is located over the center of a circular table of diameter 4 feet. Find the height h of the light source such that the illumination I at the perimeter of the table is maximum if I=k(sina)/s^2, where s is the slant height, a is the angle at which the light strikes the table, and k is a constant.

A and b are equally good tennis players

Which of the following are binary operations on S = {x ∈ R | x > 0}? Justify your
answer.
i) The operation Δ defined by xΔy = x(y− 2).
ii) The operation ∇ defined by x∇y = e^x+y.
Also, for those operations which are binary operations, check whether they are
associative and commutative.