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
What is the correlation between one's age and year of birth?
-1
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
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
The demand equation for a certain product is p=6-3q/2 dollars. Find the level of production that results in maximum revenue.
q=2
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 airline company has 350 seats available for sale in their New Dreamliner 787-8. Of these, 100 are currently sold at $300 for a one-way ticket from Tashkent to Bishkek. A market survey indicates that each $10 decrease in ticket price would result in 15 additional passengers. What price will maximize the revenue for the Airline company?
p=$183.33
3x+7y=27
5x+2y=16
Solove the SLE using Cramer's method
x=2
y=3