Algebra

Probability

Medium

applied

The probability distribution of a random discrete variable is given

X -1 0 1 2 3
P(X) 0.1 $p$ 0.3 $q$ $r$

If it is known that P(X=1) is the mean of P(X=0) and P(X=2).

Then the value of r is :

0.1

0.2

0.3

✅ Correct Option: 1

The probability distribution has some missing values:

X	-1	0	1	2	3
P(X)	0.1	$p$	0.3	$q$	$r$

P(X=1) is the mean of P(X=0) and P(X=2).

P(X=1) is the mean of P(X=0) and P(X=2):

$0.3 = \dfrac{p + q}{2}$

$p + q = 0.6$

All probabilities in a probability distribution must sum to 1:

$0.1 + p + 0.3 + q + r = 1$

$0.4 + p + q + r = 1$

$p + q + r = 0.6$

From the equations:

$p + q = 0.6$

$p + q + r = 0.6$

Therefore:

$0.6 + r = 0.6$

$r = 0$

The value of $r = 0$ .

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If two dice are rolled 12 times and getting a total greater than 4 is considered as a success, then which of the following statements are correct?

(A) The probability of getting a total greater than 4 in a single throw of the pair of dice is 5/6.

(B) Mean = 10

(D) The probability of getting a total less than or equal to 4 in a single throw of the pair of dice is 1/6.

Choose the correct answer from the options given below:

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A random variable $X$ has the following probability distribution:

X	0	1	2	3	4
P(X)	0	$\dfrac{k}{2}$	$\dfrac{3k}{2}$	$\dfrac{k}{3}$	$2k$

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Value of $k$	I.	$\dfrac{7}{13}$
B.	Value of $P(X \leq 3)$	II.	$\dfrac{3}{26}$
C.	Value of $P(X > 1)$	III.	$\dfrac{23}{26}$
D.	Value of $P(X < 2)$	IV.	$\dfrac{3}{13}$

Choose the correct answer from the options given below:

The probability distribution of a random discrete variable is given X-10123P(X)0.1ppp0.3qqqrrr If it is known that P(X=1) is the mean of P(X=0) and P(X=2). Then the value of r is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The probability distribution of a random discrete variable is given

X -1 0 1 2 3
P(X) 0.1 $p$ 0.3 $q$ $r$

If it is known that P(X=1) is the mean of P(X=0) and P(X=2).

Then the value of r is :