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Given that X₁ and X₂ have the joint density function given by f(x, y) = {2²e-1863, e-AX₂, 0<X₁ <X₂, X₂ > 0 0, otherwise Find the moment generating function of X₁ and X₂.
BAT Industries is a manufacturer of orange juice in Jamaica. In 2022 it sold a bottle of orange juice to wholesalers for $100 and its variable costs is $40 and fixed costs is $100,000 monthly:
Using the information provided.
i. How many bottles of orange juice must the company sell in order to break even and what is the breakeven revenue?
ii. If the company sold 1,500,000 bottles of orange juice for the year 2022, what was its profit?
iii. Due to inflation, in 2023 fixed costs are expected to rise to $175,000 monthly. What will be the NEW break-even quantity and revenue?
iiii. If the company will sell the same number of orange juice as it did in 2022 and it wants to make the same profit as in 20222, what price should they sell each bottle of orange Juice for in 2023?
Can some working out be shown please?
Prove or disprove: For all x ∈Z,if x mod11=5,then x 2 mod11=3.
Briefly explain different data presentation techniques.
Suppose data collected for heights (in cms) 0f 390 cows were tabulated in a frequency
distribution and thefollowing results were obtained.
fi: 6, 25, 48, 72, 116, 60, 38, 22, 3
CM1 =112, CM2=117 where CMi i
th class mark
Determine:
a. the class interval size (class width)
b. the class limits
c. class boundaries
d. class marks
e. the less than cumulative frequency distribution
f. the class intervals having the highest frequency
g. Above which height do we find 50% of the cows?
h. Below which height do we get 25% of the cows?
Draw
A. histogram
B. a frequency polygon
C. a less than ogive for the above data
Construct a frequency distribution of weights of miniature poodles if the class marks
are 6.5, 8.5, 10.5, 12.5 and 14.5 kgs with corresponding frequencies 8, 12, 22, 17 and 3.
Classify each of the following first as qualitative or quantitative and second as nominal,
ordinal, interval or ratio measure.
a) temperatures of 22 selected refrigerators
b) hair color of women on a high school tennis team
c) numbers on the shirts of a girl’s soccer team
d) ages of students in a statistics class
e) number of pages in your statistics book
f) list of 1247 social security numbers
g) the ratings of a movie ranging from “poor” to “good” to “excellent”
h) the final grades (A,B,C,D, and F) for students in a chemistry class
i) the nationalities listed in a recent survey
j) the amount of fat (in grams) in 44 cookies
Classify the following sentences as belonging to the area of descriptive statistics or
inferential statistics.
a) As a result of recent cutbacks by oil-producing nations, we can expect the price
of gasoline todouble in the next year.
b) At least 5% of all killings reported last year in city X were due to tourists.
c) Of all patients who received this particular type of drug at a clinic Y, 75%
later developedsignificant side effect.
a) The average age of the students in a statistics class is 21 years.
b) Adane concludes that his chance of passing the first year this academic year is at
least 80% basedon the statistics that 75% of the freshmen passed last year.
Given the following propositions.
Let A : Mohammad is Malaysian.
Let B : Lucy is Italian.
Formalize the following sentences using propositional logic.
i. Lucy isn’t Italian. (1 mark)
ii. If Mohammad is Italian then Mohammad is not Malaysian. (1 mark)
iii. Muhammad is Malaysian or if Mohammad isn’t Malaysian then Lucy is Italian.
(2 marks)
iv. Either Mohammad is Malaysian and Lucy is Italian, or neither Mohammad is not
Malaysian nor is Lucy Italian.
Using definition of limit, prove that
a)
b)
2. Evaluate the following limits (if exists)
a)
c)
( )
b) √
√
3. Is there a real number such that
exists? If so, find the value(s) of and
the value of the limit.
4. Find a formula for the
derivative of the following functions.
a) ( ) √ b) ( ) (
)
5. Let ( ) ( ( ( ))) ( ) ( )
( )
( )
( ) Then find
( ).
6. Find the value of so that the line is tangent to the curve
