Probability
A coin is thrown 3 times. What is the total number of possible outcomes?
8
What is the formula of Covariance?
(Sum(X-Xmean)*(Y-Ymean))/n
What are the two models in forecasting time-series data?
Additive and Multiplicative
Find the derivative of the following function:
y(x)=x2-27x+10
y'(x)=2x-27
If two matrices with the following sizes are multiplied (3x5) x (5x1), what will be the size of the resulting matrix?
(3x1)
Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards.
36/52=9/13
What is the formula of Correlation coefficient?
(Covar(x;y))/(SDx*SDy)
How do you call recurrent upward or downward movements in a time series with the period of greater than a year?
Cyclical movement
Calculate the value of the function as x approaches 0 ((x+7)2-49)/x
14
A= 5 -2
3 0
Calculate A-1
A-1= 0 1/3
-1/2 5/6
There are 5 green 7 red balls. Two balls are selected one by one without replacement. Find the probability that first is green and second is red.
35/132= 0.26
What is the correlation between one's age and year of birth?
-1 (negative)
The least-squares trend line for an annual time series on sales is: Y = 1.2 + 0.5X
What is the trend value for this time series on sales for the 10th year?
6.2
Calculate the derivative of the following function:
(x5+5x4-5)1/2
(5x4-20x3)/2(x5-5x4-5)1/2
A firm has fixed costs of $500 and a variable cost of $15 per item. It sells its product at a price of $20 per item, regardless of the number sold. At what output does the firm break even?
q=100
A coin is thrown 3 times. What is the probability that at least one head is obtained?
7/8=0.875
X 1 2 3 4 5 6 7
Y 9 8 10 12 11 13 14
Calculate the correlation coefficient (r)
r=0.93
X Y
1 3,714.24
2 3,811.15
3 3,972.89
4 4,181.17
5 4,204.11
Given that the equation function for the trendline is
y = 78.346x + 3753.8
Calculate the seasonal deviations using the additive model
1 -117.91
2 -99.34
3 -15.95
4 113.99
5 58.58
Calculate the value of the function as y approaches 7
y2-4y-21/3y2-17y-28
2/5
If the demand equation is Q = – 1.5P + 30 and the supply equation is Q = 2.5P + 20, determine the equilibrium price.
p=$2.5
A local club plans to invest $10000 to host a baseball game. They expect to sell tickets worth $15000. But if it rains on the day of game, they won't sell any tickets and the club will lose all the money invested. If the weather forecast for the day of game is 20% possibility of rain. What is the expected return?
Expected Return =5000(0.8)−10000(0.2)=4000−2000=2000
X 1 2 3 4 5 6 7
Y 9 8 10 12 11 13 14
Find the regression equation
y = 0.9286x + 7.2857
List 3 steps after calculating the trend values (T)
1. Calculate seasonal deviations
2. Calculate seasonal variations (S)
3. Add or Multiply forecasted T by the corresponding S
An apartment rental company has 800 units available for rent. Of these, 500 are currently rented at $900 per month. A market survey indicates that each $15 decrease in monthly rent would results in 10 additional rentals. What rent will produce the maximum revenue for the rental company?
P=750
3x+7y=27
5x+2y=16
Solove the SLE using Cramer's method
x=2
y=3