e?","back":"It can only take separate, countable values (e.g., 0, 1, 2).","points":1},{"id":"c86c598a-8390-400c-b79f-fbf2811e57a1","cardType":"basic","front":"If $X$ is a discrete random variable taking integer values, what is the meaning of $P(X > 1.4)$?","back":"$$P(X \\ge 2)$","points":1},{"id":"c37f75ff-38c9-4a70-b4b3-1a741ac6d6ac","cardType":"basic","front":"Define the cumulative distribution function $F(x)$ for a random variable $X$.","back":"The probability that $X$ is less than or equal to $x$: $F(x) = P(X \\le x)$.","points":1},{"id":"b1eae3e2-0fd7-4bfc-ac69-b35ed6791877","cardType":"cloze","front":"A cumulative distribution function $F(x)$ must never $\\text{[...]}$ and its final value must be $1$.","back":"A cumulative distribution function $F(x)$ must never $\\boxed{decrease}$ and its final value must be $1$.","points":null},{"id":"a7ac45e2-bb24-4d30-9e3e-ca332a111673","cardType":"cloze","front":"A cumulative distribution function $F(x)$ must never $decrease$ and its final value must be $\\text{[...]}$.","back":"A cumulative distribution function $F(x)$ must never $decrease$ and its final value must be $\\boxed{1}$.","points":null},{"id":"430faef9-9af5-45fb-879f-546547633300","cardType":"basic","front":"What characterizes a discrete uniform distribution with $n$ outcomes?","back":"Every outcome is equally likely, each with probability $1/n$.","points":1},{"id":"8d50b2c3-f791-436b-9df1-e74abdfe56aa","cardType":"basic","front":"State the four conditions required for a binomial distribution $X \\sim B(n, p)$.","back":"

Fixed number of trials ($n$)
Two outcomes: success or failure
Constant probability of success ($p$)
Trials are independent

","points":3},{"id":"db059962-af03-45c9-9ad3-8ede43901547","cardType":"basic","front":"In the notation $X \\sim B(n, p)$, what do $n$ and $p$ represent?","back":"

$n$: number of trials
$p$: probability of success

","points":2},{"id":"b11ff88c-05c1-4e0f-a2d4-b1e6cef8ff4e","cardType":"cloze","front":"The probability of exactly $r$ successes in a binomial distribution is $P(X=r) = \\text{[...]}$.","back":"The probability of exactly $r$ successes in a binomial distribution is $P(X=r) = \\boxed{\\binom{n}{r}p^r(1-p)^{n-r}}$.","points":null},{"id":"bb0a3105-60e0-49ba-8a2e-be25ecfc5c06","cardType":"basic","front":"How is the binomial inequality $P(X < 3)$ rewritten for calculator entry (using cumulative functions)?","back":"$$P(X \\le 2)$","points":1},{"id":"761d49fe-0c33-4963-878a-07f5d2491a02","cardType":"basic","front":"How is $P(X \\ge 5)$ calculated using the complement rule in a binomial model?","back":"$$1 - P(X \\le 4)$","points":1},{"id":"7e8b8672-745f-4e89-bbca-f509ed4b9b6f","cardType":"basic","front":"Why might \"number of goals in a football match\" not be well-modelled by a binomial distribution?","back":"

Events are not independent
Probability of scoring is not constant throughout the match

","points":2},{"id":"30da9dc6-6e0f-48e7-a865-03d6a6001df0","cardType":"basic","front":"What is the formula for the expected number of successes if an event with probability $p$ is repeated $N$ times?","back":"$$Np$","points":1},{"id":"a67018cf-9323-4b96-9b46-1a6207a50bf3","cardType":"cloze","front":"An expected value $Np$ is a $\\text{[...]}$ and does not have to be a $whole number$.","back":"An expected value $Np$ is a $\\boxed{long-run average}$ and does not have to be a $whole number$.","points":null},{"id":"d84c6b33-e908-4625-8c8e-54c74b0e59d6","cardType":"cloze","front":"An expected value $Np$ is a $long-run average$ and does not have to be a $\\text{[...]}$.","back":"An expected value $Np$ is a $long-run average$ and does not have to be a $\\boxed{whole number}$.","points":null},{"id":"7c293a90-9696-4c7d-8c8a-4db801

Statistical Distributions Flashcards

Statistical Distributions Flashcards

Statistical Distributions Flashcards

Statistical Distributions Flashcards