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Two fair cubical dice are thrown: one is red and one is blue. The random variable
M represents the score on the red die minus the score on the blue die.
a. Find the distribution of M.
b. Write down E(M).
c. Find Var (M)
Differentiate between ‘discrete’ and ‘continuous’ random variables with
appropriate examples.
Why normal curve is useful in problem solving. Give a real life situation as your own example?
The value of a delivery van depreciates at the rate of 15% per year. Show that
annual depreciation follows a geometric progression, and use this progression
to determine the value of the van after three years, if it is purchased for $4500?
What is the freezing point depression of an aqueous solution that contains 3m of ionic solute CaCl2 per 1 kg of water. The freezing point depression constant for water is -1.86 degree Celsius per mole (* CaCl2 dissociates into 3 ions)
Find the multiplicative inverse of 197 modulo 3000. Highlight each step clearly.
Cyclopentaethiol has a markedly lower melting point than cyclopentanol even though, it has a higher molecular weight. Explain
Use the Euclidean algorithm to find the Greatest Common Divisor of:
a. 1819 and 3587 b. 42823 and 6409
Use factor trees to find the GCF and LCM of the following:
a. 24 and 60 b. 150, 210 and 375
Program in Java
PROGRAM DESIGN
Create a class Date that can perform the following operations on a date:
- Set/Return the Month
- Set/Return the Day
- Set/Return the Year
- Whether the year is a leap year.
if the year number isn't divisible by 4, it is a common year;
otherwise, if the year number isn't divisible by 100, it is a leap year;
otherwise, if the year number isn't divisible by 400, it is a common year;
otherwise, it is a leap year.
- Return the number of days in a month
April, June, September, November has 30 days otherwise 31 except for Feb (refer to leap year)
- Print the month in string format followed by the date and year
SAMPLE INPUT1
2020
2
15
SAMPLE OUTPUT1
February 15, 2020
29 days
2020 is a Leap Year
SAMPLE INPUT2
2019
2
29
SAMPLE OUTPUT2
Invalid number of days
SAMPLE INPUT3
2019
3
15
SAMPLE OUTPUT3
March 15, 2019
31 days
2019 is a Common Year
#339914 on Dec 2023