Home
Class 12
MATHS
Let X denote the no. of hours you study ...

Let X denote the no. of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where `lamda` is some unknown constant.

(a) Find the value of `lamda`
(b) What is the probability that you study at least two hours ? Exactly two hours? At most two hours?

Text Solution

Verified by Experts

The probability distribution of X is

(a) We known that `sum_(i=1)^(n)P_i=1`
therefore `0.2+lamda+2lamda+3lamda+2lamda=1`
`8lamda=0.8`
`lamda=0.1`
(b) P(you study at least two hours) `=P(Xgt=2)`
= P(X=2)+P(X=3)+P(X=4)
=`2lamda+3lamda+2lamda=7lamda=0.7`
P(you study exactly two hours) = P(X=2)
`=2lamda=0.2`
P(you study at most hours)`=P(Xlt=2)`
=P(X=0)+P(X=1)+P(X=2)
`=0.2+lamda+2lamda`
=0.2+0.3=0.5
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    AAKASH INSTITUTE ENGLISH|Exercise TRY YOURSELF|42 Videos

  • PROBABILITY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - A Competition Level Questions)|114 Videos

  • PRINCIPLE OF MATHEMATICAL

    AAKASH INSTITUTE ENGLISH|Exercise Section-D:(Assertion-Reason Type Questions)|11 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

Similar Questions

Explore conceptually related problems

Let X denote the number of hours you study during a randomly selected school day The probability that X can take the values x. has the following form, where k is some unknown constant. P(X=x)={0. 1 if x=0,k x if x=1 , 2k(5-x) if x=3 or 4, 0 otherwise

Let X denote the number of hours you study during a randomly selected school day. The probability that X take the values of x has the following form, where k is some unknown constant. P(X=x)={(0.1 "if" x=0),(kx, "if" x=1 "or"2),(k(5-x),"if"x=3"or"4),(0,"otherwise"):} Find: (i) k (ii) the probability that you study exactly two hours, (iii) the probability that you study at most two hours.

Let, X denote the number of colleges where you will apply after your results and P (X = x) denotes your probability of getting admission in x number of colleges. It is given that P(X=x)={k x;ifx=0or1, 2k x;ifx=2,k(5-x), ifx=3or4, 0;ifx >4 where k is a positive constant. Find the value of k . Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.

A cyclist maintains a constant speed on his bicycle . The graph above shows the number of miles he covers in x hours . Two points on the graph are (2,10) and (3,15). What is the cyclist's speed in miles per hour ?

Two numbers are selected at random (without replacement) from positive integers 2,3,4,5,6, and 7 . Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X .

Two numbers are selected are random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X.

(i)If fuor squares are chosen at random on a chess board, find the proability that they lie on diagonal line. (ii) If two squares are chosen at random on a chess board, what is the Probability that they have exactly on corner in common? (ii) If nine squares are chosen at random on a chess board, what is the probability that they form a square of size 3x3?

A well-watered healthy potted plant with variegated leaves was kept in darkness for about 24 hours. It was then set-up as shown in the diagram below and exposed to light for about 12 hours. At the end of this time, leaf X and leal y were tested for starch. Study the diagram and answer the questions that follow Select the correct leaf from the five available choices shown in the diagram as A, B, C, D and E Rewrite the correct answer by filling in the appropriate letter for the questions that follow : After the starch test, leaf X would look like ........

A well-watered healthy potted plant with variegated leaves was kept in darkness for about 24 hours. It was then set-up as shown in the diagram below and exposed to light for about 12 hours. At the end of this time, leaf X and leal y were tested for starch. Study the diagram and answer the questions that follow Select the correct leaf from the five available choices shown in the diagram as A, B, C, D and E Rewrite the correct answer by filling in the appropriate letter for the questions that follow : After the starch test, leat Y would look like ................

A bag contains 18 balls out of which x balls are red. (i) If one ball is drawn at random from the bag what is the probability that it is not red? (ii) If two more red balls are put in the bag, the probability of drawing a red ball will be (9)/(8) times the probability of drawing a red ball in the first case. Find the value of x.