Mean and Variance of a Random Variable

JEE Main Mathematics · Probability · 17 questions, latest first

• The probability distribution of a random variable X is given below: If E(X)=263/15, then P(X<20) is equal to:202628 January, Shift 2 · Q8
• A random variable X takes values 0, 1, 2, 3 with probabilities (2 a+1)/30, (8 a-1)/30, (4 a+1)/30, b respectively, where a, b ∈…202621 January, Shift 2 · Q10
• Let a random variable X take values 0,1,2,3 with P(X=0)=P(X=1)=p, P(X=2)=P(X=3) and E(X^2)=2 E(X). Then the value of 8 p-1 is:20257 April, Shift 2 · Q9
• A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective…20254 April, Shift 1 · Q9
• Let A=[a_i j] be a 2 × 2 matrix such that a_i j ∈{0,1} for all i and j. Let the random variable X denote the possible values of…202529 January, Shift 2 · Q9
• Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate…202528 January, Shift 1 · Q8
• A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ^2 denote the mean and variance…202522 January, Shift 1 · Q8
• Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively…20248 April, Shift 1 · Q30
• From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the…20246 April, Shift 2 · Q29
• Let the mean and the standard deviation of the probability distribution be μ and σ, respectively. If σ-μ=2, then σ+μ is equal to…20245 April, Shift 2 · Q29
• From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote…20245 April, Shift 1 · Q30
• If the mean of the following probability distribution of a radam variable X: is 46/9, then the variance of the distribution is20244 April, Shift 2 · Q19
• Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten…202431 January, Shift 1 · Q17
• A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur.…202313 April, Shift 1 · Q18
• Two dice A and B are rolled. Let the numbers obtained on A and B be α and β respectively. If the variance of α-β is p/q, where p…202312 April, Shift 1 · Q18
• A fair n(n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is…202312 April, Shift 1 · Q30
• Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the…202329 January, Shift 1 · Q79