Question23:-The joint pdf of a bivariate random variable (X, Y) is given by
“f(x, y) = 4xye*(-(x*(2)+y*(2)),, “x>= 0, y>=0"
The pdf of ‘U=sqrt(X*(2)+Y*(2))* will be
A:-g(u)=(2)/(u%(3)).e*(-u*(3)), ௩-0”
8:-` g(u)=2u%(3).e*(-u%(3)), ௨-0”
C:-'g(u)=(2)/(u*(3))e*(-u*(2)), u>=0°
D:-'g(u)=2u%(3).e*(-u*(2)), u>=0°
Correct Answer:- Option-D
Question24:-The degrees of freedom of the ‘chi*(2)° statistics for testing the independence of attributes of a data
expressed as a 5 x 4 contingency table will be
A:-20
B:-12
C:-18
D:-19
Correct Answer:- Option-B
Question25:-A statistical test for testing “H_(0):theta=theta_(0)* against “H_(1):theta=theta_(1)° with type | error
probability ‘alpha* and type Il error probability ‘beta* is said to be unbiased, if
A:- alpha<=1-beta*
8:- alpha>=1-beta”
C:-’ L-alpha!=beta’
D:-None of these
Correct Answer:- Option-A
Question26:-If the p-value of a test is 0.04, which of the following statement is true ?
#:-॥ (0) can be rejected at 1% level of significance
B:-'H_(0)* can be rejected at 5% level of significance
C:-Both 1 and 2 are true
D:-Both 1 and 2 are false
Correct Answer:- Option-B
Question27:-The sum of two independent exponential random variables with parameter ‘Lambda* will have
A:-Exponential distribution
B:-Beta distribution
C:-Gamma distribution
D:-None of these
Correct Answer:- Option-C
Question28:-If *X_(1)° and *X_(2)* are two independent Poisson random variables with parameters ‘Lambda_(1)°
and ‘Lambda _(2)° respectively, the distribution of *X_(1)-X_(2)° will be
A:-Poisson with parameter ‘Lambda_(1)-Lambda_(2)*
B:-Poisson with parameter ‘Lambda_(1)+Lambda_(2)°
C:-Binomial with parameter *Lambda_(1)-Lambda_(2)°
D:-None of these
Correct Answer:- Option-D
Question29:-"A function 9 on R is a characteristic function if and only if it is non-negative definite and continuous". This
theorem is known as
A:-Scheffe's theorem
B:-Bochner's theorem
C:-Helly-Bray theorem
D:-None of these
Correct Answer:- Option-B
Question30:-For a normal population with mean ‘mu’ and variance ‘Sigma*(2)*, the hypothesis *H_(0):mu=mu_(0),
Sigma>Sigma_(0)° is a
A:-Simple hypothesis
B:-Composite hypothesis
C:-Neither simple nor composite
D:-None of these
Correct Answer:- Option-B
Question31:-Wald-Wolfowitz run test is used to test
A:-Median of two populations are same
B:-Mean of two populations are same
C:-Variance of two populations are same
D:-Samples are from same population or not