frojeostern

Two dice are thrown simultaneously. if x denotes the number osixes, find the expectation of x.

1 Jahrs vor

Kommentare: 0

Ansichten: 64

Solution

Long Answer

When a dice is rolled once, probability of obtaining six =

and probability of obtaining a non-six =

Now X can take values 0, 1, 2.P(X = 0) = P(six does not appear a die) = P(non-six on both dice)

P(X = 1) = P(six appear exactly on one die) = P(six on first die and non-six on the second die) + P(six on the second die and non-six on the first die)

P(X = 2) = P(six on both the dice) =

∴ probability distribution of X is

∴ Expectation of X = mean of the variable X

Your browser is no longer supported. Update it to get the best YouTube experience and our latest features. Learn more

Remind me later

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Page 2

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

Buy Now

>

Two die are thrown simultaneously. If X denote the number sixes, find the expectation of X.

Solution

Let X be the random variable which denotes the number of sixes on two dice. So, X may have values 0,1 or 2.

When a dice is rolled once, probability of obtaining six $= \frac{1}{6}$ and probability of obtaining a non-six $= \frac{5}{5}$

P(X =0) =P (non-six on both dice)= $\frac{5}{6} \times \frac{5}{6} = \frac{25}{36}$

P(X=1)=P (six on first and non -six on the second)+P(non-six on the first and six on the second)

$= \frac{1}{6} \times \frac{5}{6} + \frac{1}{6} \times \frac{5}{6} = \frac{10}{36}$

P(X=2)=P(six on both the dice) $= \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$

Therefore, the required probability distribution is as follows:

$\begin{matrix} X & 0 & 1 & 2 P (X) & \frac{25}{36} & \frac{10}{36} & \frac{1}{36} \end{matrix}$

$∴$ Expectation of X=mean of the variable X

= $\sum X P (X) = 0 \times \frac{25}{36} + 1 \times \frac{10}{36} \times + 2 \times \frac{1}{36} = \frac{12}{36} = \frac{1}{3} .$

Suggest Corrections

1