To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation(1) with μ = 5 and (A) μ = 10 (B) μ = 15 (C) μ = 20 Graph all three in the same viewing window with X min = − 10 , X max = 40 , Y min = 0 and Y max = 0.1
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation(1) with μ = 5 and (A) μ = 10 (B) μ = 15 (C) μ = 20 Graph all three in the same viewing window with X min = − 10 , X max = 40 , Y min = 0 and Y max = 0.1
Solution Summary: The author analyzes the equation of normal distribution. f(x)=1sigma
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean
µ
and standard deviation
σ
:
f
x
=
1
σ
2
π
e
−
x
−
μ
2
/
2
σ
2
Graph equation(1) with
μ
=
5
and
(A)
μ
=
10
(B)
μ
=
15
(C)
μ
=
20
Graph all three in the same viewing window with
X
min
=
−
10
,
X
max
=
40
,
Y
min
=
0
and
Y
max
=
0.1
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
(a) Define the notion of an ideal I in an algebra A. Define the product on the quotient
algebra A/I, and show that it is well-defined.
(b) If I is an ideal in A and S is a subalgebra of A, show that S + I is a subalgebra
of A and that SnI is an ideal in S.
(c) Let A be the subset of M3 (K) given by matrices of the form
a b
0 a 0
00 d
Show that A is a subalgebra of M3(K).
Ꮖ
Compute the ideal I of A generated by the element and show that A/I K as
algebras, where
0 1 0
x =
0 0 0
001
(a) Let HI be the algebra of quaternions. Write out the multiplication table for 1, i, j,
k. Define the notion of a pure quaternion, and the absolute value of a quaternion.
Show that if p is a pure quaternion, then p² = -|p|².
(b) Define the notion of an (associative) algebra.
(c) Let A be a vector space with basis 1, a, b. Which (if any) of the following rules
turn A into an algebra? (You may assume that 1 is a unit.)
(i) a² = a, b²=ab = ba 0.
(ii) a²
(iii) a²
=
b, b² = abba = 0.
=
b, b²
=
b, ab = ba = 0.
(d) Let u1, 2 and 3 be in the Temperley-Lieb algebra TL4(8).
ገ
12
13
Compute (u3+ Augu2)² where A EK and hence find a non-zero x € TL4 (8) such
that ² = 0.
Q1: Solve the system x + x = t², x(0) = (9)
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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