Applied Mathematics

Probability Distribution

Medium

$P(X = x) = \begin{cases} 2k & \text{if } x = 0 \\ kx & \text{if } x = 1 \\ k(x - 1) & \text{if } x = 2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The value of k is

$\frac{1}{4}$

$\frac{1}{6}$

$\frac{2}{3}$

✅ Correct Option: 2

We know that $x$ can only take values $0, 1, 2, 3$ since $P(X = x) = 0$ for everything else.

$P(X = 0) = 2k$

$P(X = 1) = k(1) = k$

$P(X = 2) = k(2 - 1) = k$

$P(X = 3) = k(3 - 1) = 2k$

For any probability distribution, the sum of all probabilities must always equal $1$ (since one of the outcomes has to happen).

$P(X=0) + P(X=1) + P(X=2) + P(X=3) = 1$

$2k + k + k + 2k = 1$

$6k = 1$

$k = \dfrac{1}{6}$

2026: 30 May Shift 2

There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

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If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success is

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In a binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of 3 successes is

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There are 50 telephone lines in an exchange. If the probability that any one of them will be busy is 0.1, then the probability that all the lines are busy is

2023: 11 Aug Shift 1

A random variable X has a probability distribution P(X) of the following form, where k is some unknown constant:

P(X = 0) = k

P(X = 1) = 2k

P(X = 2) = 3k

P(X = other values) = 0

Then, find the value of 1/k.

2023: 7 June Shift 1

If the mean of a binomial distribution is 24 and its standard deviation is 4 , then the probability of getting success is :

P(X=x)={2kif x=0kxif x=1k(x−1)if x=2 or 30otherwiseP(X = x) = \begin{cases} 2k & \text{if } x = 0 \\ kx & \text{if } x = 1 \\ k(x - 1) & \text{if } x = 2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}P(X=x)=⎩⎨⎧​2kkxk(x−1)0​if x=0if x=1if x=2 or 3otherwise​ The value of k is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

$P(X = x) = \begin{cases} 2k & \text{if } x = 0 \\ kx & \text{if } x = 1 \\ k(x - 1) & \text{if } x = 2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The value of k is