If x is a continuous random variable with p.d.f.
ƒ(x) = 1/√2∏ exp (-x2/2), -∞ < x < ∞
and y is defined as y = x+1, then E(y) equals:
If a variable has three values k, 0 and 3k with corresponding frequencies as 3k, 2k and k respectively, then the value of coefficient of skewness b1 is :
The joint distribution of x and y is as follows
Then E(x|y=1) is :
The mean and standard deviation of a variable x are 36 and 4 respectively. Then the mean and standard deviation of [50 (x/4)], respectively are :
Let x ~ Binomial (5,0.6) and Y ~ Poisson (2) be independent. Then P(xy = 0) equals :
In a negatively skewed distribution
If a continuous random variable x has the probability density function
For a frequency distribution of a discrete variable, the diagram of less than type cumulative frequency is a
It is known from past experience that in a certain plant there are on the average 4 industrial accidents per month. The probability that in a given month there will be less than 4 accidents is : (e4= 0.0183)
For a frequency distribution of a variable x, mean = 32, median = 30. The distribution is :
Let x be a random variable with probability mass function
ƒ(x) = k, |x|, if x = -2, 1, 3
=0, otherwise
where, K is a constant. Then the variance of x is :
If L(p) and L(q) represent Laspeyres' index number for prices and quantities and P(p) and P(q) represents Paasche's index number for price and quantities then :
Initially there are 9 workers, all being paid a uniform wage. Later a 10th worker is added whose wage rate is Rs 20 less than for the others. The average wage gets :
Event S and T are independent with P(S) < P(T), P(S ∩ T) = 6/25 and P(S|T) + P(T|S) = 1. Then P(S) is
The formula for calculating an index number should be such that it gives the same ratio between one point of comparison and the other, no matter which of the two is taken as the base or putting it another way, the index number reckoned forward should be reciprocal of the one reckoned backwards' which test of consistency of index number is this ?
The system of combining two or more overlapping series of index numbers to obtain a single continuous series is called
If 'I' represents a cost of living index, then the purchasing power of money is proportional to
The standard deviation of a distribution is 5. The value of the fourth central moment, in order that the distribution be mesokurtic, should be :
Suppose owing to increased prices, a consumer reduces consumption of all commodities by 10% compared to the previous year. If IL and IP are the Laspeyres' and Paasche's price indices for the current year with the previous year as base, then
The probability that an urn containing 5 balls contains only white balls if the first two balls drawn from it were found to be white is :
If the trend equation fitted from a data on production (y in kg) of a fertilizer factory is 26y = 5335 + 624t, where time(t) has unit 1 year. Then monthly increase in production of fertilisers (in kg) is:
Let E and F be two events with P(E ) > 0, P(F|E) = 0.3 and P(E ∩ Fc ) = 0.2. Then P(E) equals:
The annual vehicles production (In lacs) in India is given in the pie chart.
If the annual production of motor cycle is 1.80 lacs, the annual production
Link relatives in a time series remove the influence of :
A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36, then P(A) and P(B), respectively are :
If the actual values in time series from 2000 to 2006 are 77, 88, 94, 85, 91, 98 and 90 and the equation of the trend line with 2003 as origin is Y = 89 + 2X , then in case of multiplicative model, the trend eliminated values are :
If a time series data is given below then find three yearly moving averages to find trend.
Which one of the options is correct:
The probability that a contractor gets a plumbing contract is 2/3 and the probability that he will not get an electric contract is 5/9. If the probability of getting at least one contract is 4/5, then the probability that he will get both the contracts is :
In time series analysis which source of variation can be estimated by the ratiototrend method:
If the arithmetic mean is 26.8 and the median is 27.9, then the mode is :