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Let be the discrete random variable representing the number appeared on the face of a biased die when it is rolled. The probability distribution of is
Then variance of is

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Important Questions on Probability
MEDIUM
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IMPORTANT
unbiased coins are tossed. The probability of having the number of heads is not equal to the number of tails is

HARD
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IMPORTANT
Let represent the probability mass function of a Poisson distribution. If its mean then value of at which is maximum is

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A random variable takes the values and such that . If is the variance and is the mean of , then

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As a business strategy, of the new internet service subscribers selected randomly receive a special promotion. If a group of such subscribers signs for the service, then the probability that at least two of them get the special promotion is

MEDIUM
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IMPORTANT
In a communication network, ninety-eight percent of messages are transmitted with no error. If a random variable denotes the number of incorrectly transmitted messages, then the probability that atmost one message is transmitted incorrectly out of 500 messages sent, is

EASY
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IMPORTANT
If the probability that an individual will suffer a bad reaction from an injection is then the probability that out of individuals, exactly individuals suffer a bad reaction is

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IMPORTANT
A fair coin is tossed times. The probability that the tail will appear atleast thrice is

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If '' is the mean of a Poisson distribution, then
