The shelf life (in years) of a laser pointer battery is a continuous random variable with probability density function f ( x ) = { 1 / ( x + 1 ) 2 i f x ≥ 0 0 otherwise (A) Find the probability that a randomly selected laser pointer battery has a shelf life of 3 years or less. (B) Find the probability that a randomly selected laser pointer battery has a shelf life of from 3 to 9 years. (C) Graph y = f ( x ) for [0, 10] and show the shaded region for part (A).
The shelf life (in years) of a laser pointer battery is a continuous random variable with probability density function f ( x ) = { 1 / ( x + 1 ) 2 i f x ≥ 0 0 otherwise (A) Find the probability that a randomly selected laser pointer battery has a shelf life of 3 years or less. (B) Find the probability that a randomly selected laser pointer battery has a shelf life of from 3 to 9 years. (C) Graph y = f ( x ) for [0, 10] and show the shaded region for part (A).
Solution Summary: The author explains that the probability of a randomly selected laser pointer battery having 3 years or less is 0.75.
these are solutions to a tutorial that was done and im a little lost. can someone please explain to me how these iterations function, for example i Do not know how each set of matrices produces a number if someine could explain how its done and provide steps it would be greatly appreciated thanks.
Q1) Classify the following statements as a true or false statements
a. Any ring with identity is a finitely generated right R module.-
b. An ideal 22 is small ideal in Z
c. A nontrivial direct summand of a module cannot be large or small submodule
d. The sum of a finite family of small submodules of a module M is small in M
A module M 0 is called directly indecomposable if and only if 0 and M are
the only direct summands of M
f. A monomorphism a: M-N is said to split if and only if Ker(a) is a direct-
summand in M
& Z₂ contains no minimal submodules
h. Qz is a finitely generated module
i. Every divisible Z-module is injective
j. Every free module is a projective module
Q4) Give an example and explain your claim in each case
a) A module M which has two composition senes 7
b) A free subset of a modale
c) A free module
24
d) A module contains a direct summand submodule 7,
e) A short exact sequence of modules 74.
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Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
Chapter 6 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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