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WorksheetsStatistically Speaking by SIAM VIT
Total questions: 20
Worksheet time: 30mins
Two random variables X and Y have the joint density function as given in the image. Find the constant K. (Provide the numeric value)
(a)
In a symmetric distribution
mean ≠ median ≠ mode
mean = median = mode
mean > median > mode
mean< median < mode
A store has 10 Samsung TVs, 3 Sony and 2 LG TVs. Two TVs are chosen at random. The probability that atleast one is Samsung is
0.905
0.904
0.476
0.375
In which pair is the number of cereals grown equal?
1996 and 1997
1998 and 2000
1999 and 1994
Insufficient data
If the coefficient of correlation between two variables x and y is 0.75 and the regression coefficient x on y is 0.8, then regression coefficient y on x be (a) . (Give only numerical value upto 1 decimal place)
If X is a continuous random variable and E(X) = 3, then E((3^2)X) is? (Give only numerical value)
(a)
An insurance company has estimated the following cost probabilities for the next year on a particular model car. The expected cost to the insurance company is (approximately)
700
750
800
850
In a distribution, standard deviation is 10. All observation added by 5 would give the result to standard deviation as? (Give only numerical value)
(a)
What is P(0 < X < 3)?
8/81
0.987
8/80
0.997
The scatterplot below shows data points and the regression line for predicting y from x. Which statement is true about the effect of removing point A or B on the regression model?
Removing A would decrease the slope but removing B would increase the slope.
Removing A would increase the slope but removing B would have little effect on the slope.
Removing A would decrease the correlation but removing B would increase the correlation.
Removing point A would increase the correlation and removing point B would not change the correlation.
For a Binomial distribution, the mean is 30 and Standard deviation is 5, then number of trials will be? (Numeric value only)
(a)
For the given data 5,10,17,24,30, the Harmonic mean is
11.5
21.5
31.5
41.5
In a colony, 60% of houses have air conditioning. A group of 8 houses is chosen at random. Find the probability that exactly 5 have air conditioning.
0.279
0.330
0.390
0.597
For the density function f(x) = 2x/9, for 0<x<3 the mean is? (Give numeric value only)
(a)
If a random variable X is defined such that E[(X − 1)²] = 16 and E[(X − 2)²] = 12, find μ and σ².
3.6 and 9.756
7/2 and 39/4
7/3 and 37/4
2.34 and 9.45
Let X be a random variable with the probability distribution as shown in figure. Find the expected value of Y= (X-1)2. (Provide numerical value only)
(a)
The mean of a random variable X is 8, then E(4X+2) is (a) . (provide numerical value only)
Let’s say that a store X has 4 yellow and 5 white shirts in stock and store Y has 6 yellow and 3 white shirts. A random shirt from the store X is transported to store Y. After 2 days, a shirt is bought at random from among those now in store Y. What is the probability a white shirt was transported from store X to store Y given that the shirt bought from store Y is yellow?
14/29
1/2
7/10
15/29
Suppose that SIAM team has 30 members excluding the faculty coordinator. The average weight of the SIAM team after including the weight of the faculty coordinator is 31 kg. What is the weight of the faculty coordinator if the average weight of the members increases by 1 kg when the weight of the faculty coordinator is added? (Provide only numerical value. Weight units should not be included in answer.)
(a)
Arjun is working as a data scientist. He is confused between L1 and L2 regularization. Choose the appropriate option(s) to help him get clarity on the concepts.
Both L1 and L2 regularization will help in overfitting to the training data.
L1 and L2 regularization will have different penalties to the cost.
If Arjun works on high dimensional data, with extensive features, L1 would be a good option.
Both L1 and L2 regularization will help in underfitting to the training data.
