Mathematics Assignment- Probability

Mathematics Assignment:
Student Name:
Instructor Name:
Course Number:
16th April 2020

Q1)
a)Probability is the chance of an event occurring.
Kinds of probability.
They include
 Classical probability
It has elements that have equal chances of happening.
 Empirical probability
Is a ratio comparing number of outcomes of an event to the total trials.
 Subjective probability
Is based on one’s judgment or experience of an event occurring.
 Axiomatic probability
A set of rules applying to all probabilities is set.
b)
There are four possible outcomes i.e. HH, HT, TH and TT
i) P (A) = P (Getting one H maximum) = P(HT ∨TH )= 2
4 = 1
2
ii) P (B) = P (Getting no H at all) =P ( TT )= 1
4
Q2)
a) Random variable is a variable having values that relies on the outcomes of a casual
phenomenon.

b) The expected value is obtained as follows
E( x )=0 (0.35)+ 1(0.20)+ 2(0.25)+ 3(0.15)+4 (0.05)
¿ 0+0.20+ 0.50+0.45+0.20=1.35
Expected value=1.35
Q3)
a) Central Limit Theorem
It states that from a population having mean μ and standard deviation σ and adequately large
samples drawn from that population while doing replacement, and then the sample means
distribution will be approximately having normal distribution (Broemeling, 2011).
b)
The standard error of the sample mean is calculated as follows
σ =1∧n=40
σ x= σ
√ n = 1
√ 40
σ x=0.1581
Q4)
Estimation is where statistics are divided and processing of signals done with an aim of
ascertaining the values of parameters using data that is measured and the empirical one
(Shumway & Stoffer, 2017).