1
GATE CE 2024 Set 2
+2
-0.833

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by 50%. Medicine X is taken by 50 of these 100 patients. The probability that a randomly selected patient, out of the 100 patients, takes medicine X and has a heart attack is

A

40%

B

60%

C

20%

D

30%

2
GATE CE 2024 Set 1
Numerical
+2
-0.833

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the probability that it will be exceeded at least once in 50 years is ______________ % (rounded off to the nearest integer).

3
GATE CE 2017 Set 1
+2
-0.6
For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which one of the following statements is correct?
A
$$a = 1,\,b = 4$$
B
$$\,a = 0.5,\,b = 1$$
C
$$a=0,$$ $$b=1$$
D
$$a=1,$$ $$b=-1$$
4
GATE CE 2016 Set 2
+2
-0.6
If $$f(x)$$ and $$g(x)$$ are two probability density functions, $$f\left( x \right) = \left\{ {\matrix{ {{x \over a} + 1} & : & { - a \le x < 0} \cr { - {x \over a} + 1} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$$$g\left( x \right) = \left\{ {\matrix{ { - {x \over a}} & : & { - a \le x < 0} \cr {{x \over a}} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$

Which of the following statements is true?

A
Mean of $$f(x)$$ and $$g(x)$$ are same; Variance of $$f(x)$$ and $$g(x)$$ are same .
B
Mean of $$f(x)$$ and $$g(x)$$ are same ; Variance of $$f(x)$$ and $$g(x)$$ are different.
C
Mean of $$f(x)$$ and $$g(x)$$ are different ; Variance of $$f(x)$$ and $$g(x)$$ are same .
D
Mean of $$f(x)$$ and $$g(x)$$ are different; Variance of $$f(x)$$ and $$g(x)$$ are different.
EXAM MAP
Medical
NEET