1. The numbers of claims which have arisen in the last twelve years on 60 motor car policies (continuously in force over this period) are shown (sorted) below 0 0000 00 000 0 0 1 1111112222 2 2222 22 3 33 3333 3 3 3 444 4 4555 5 6 6 6 7 1111 (a) Draw a barplot of the number of claims. (b) Calculate the median, mode and mean of the data. (c) Calculate the interquartile range and the standard deviation of the data.
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
![1. The numbers of claims which have arisen in the last twelve years on 60 motor car
policies (continuously in force over this period) are shown (sorted) below
0 0 00 0 0 0 0 0 0 0 0 1 1 1 11 1 11
111111 22 2 2 2 2 2 2 2 22 3 3 3
33 3 3 3 3 3 44 44 4555 5 6 6 6 7
(a) Draw a barplot of the number of claims.
(b) Calculate the median, mode and mean of the data.
(c) Calculate the interquartile range and the standard deviation of the
data.
2. Let X1, X2, ,X, be a random sample of size n from an Exp(1/0) distribution (i.e
with mean 0 and variance 62).
(a) Derive an expression for E(X) and Var(X) in terms of 0 where X is the mean of
the random sample.
[3]
(b) Express MSE(X) in terms of Var(X) and Bias (X) and hence find an expression
for MSE(X) in terms of 0.
(c) Consider the family of estimators for 0 of the form Y aX.
Find MSE(aX) and determine the value of a' such that Y = a'X is the most
efficient estimator of the form Y = aX.
3. Let X1, X2, ,X, be a random sample from the probability distribution
0;0<x<1
f(z,0) =
otherwise
where the parameter 0 > 0.
(a) Find E [X] for this distribution
(b) Use the method of moments (MME) to find an estimator for 0
(c) Find the maximum likelihood estimator (MLE)for 0.
(d) Calculate the estimate using the MME and MLE estimators when
= 0.10, r = 0.22, r3 0.54, = 0.36](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbea9d03-e0eb-4d48-beb5-27420e56a67f%2Fff766255-47b0-4aa3-bc7a-994f2797afc3%2Folp7yab_processed.jpeg&w=3840&q=75)
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