$A$ random variable $X$ has the following probability distribution:
$X = x$$1$$2$$3$$4$$5$$6$$7$$8$
$P(X = x)$$0.15$$0.23$$k$$0.10$$0.20$$0.08$$0.07$$0.05$

For the events $E = \{x : x \text{ is a prime number}\}$ and $F = \{x : x < 4\}$, then $P(E \cup F) = $

  • A
    $0.57$
  • B
    $0.87$
  • C
    $0.77$
  • D
    $0.35$

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$X$$1$$2$$3$$4$$5$
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If on an average $4$ customers visit a shop in an hour, then the probability that more than $2$ customers visit the shop in a specific hour is

$A$ random variable $X$ takes the values $1, 2, 3$ and $4$ such that $2 P(X=1) = 3 P(X=2) = P(X=3) = 5 P(X=4)$. If $\sigma^2$ is the variance and $\mu$ is the mean of $X$, then $\sigma^2 + \mu^2 =$

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